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<h3>Contents</h3>
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<div class="h2"><a href="#most-popular"> Most Popular Decimals Worksheets this Week</a></div>
<div class="h2"><a href="#decimal-grids-charts">Grids and Charts Useful for Learning Decimals</a></div>
<div class="h2"><a href="#decimals-expanded-form">Decimals in Expanded Form</a></div>
<div class="h2"><a href="#rounding-decimals">Rounding Decimals Worksheets</a></div>
<div class="h2"><a href="#comparing-ordering-decimals">Comparing and Ordering/Sorting Decimals Worksheets.</a></div>
<div class="h2"><a href="#converting-decimals">Converting Decimals to Fractions and Other Number Formats</a></div>
<div class="h2"><a href="#adding-subtracting-decimals">Adding and Subtracting Decimals</a></div>
<div class="h2"><a href="#multiplying-dividing-decimals">Multiplying and Dividing Decimals</a></div>
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<p class="firstp">Thanks for visiting the Decimals Worksheets page at Math-Drills.Com where we make a POINT of helping students learn. On this page, you will find <span itemprop="description">Decimals worksheets on a variety of topics including comparing and sorting decimals, adding, subtracting, multiplying and dividing decimals, and converting decimals to other number formats.</span> To start, you will find the general use printables to be helpful in teaching the concepts of decimals and place value. More information on them is included just under the sub-title.</p>
<p>Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. There are many operations with decimals worksheets throughout the page. It would be a really good idea for students to have a strong knowledge of addition, subtraction, multiplication and division before attempting these questions.</p>
<div class="popular">
<h2 id="most-popular"><svg class="iconwhite size32 iorange"><use xlink:href="includes/symbol-defs.006.svg#icon-fire"></use></svg> Most Popular Decimals Worksheets this Week</h2>
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<a href="decimal/decimals_multiplication_0302_various_various_001.html" title="Multiplying 3-Digit by 2-Digit Numbers with Various Decimal Places"><figure><img src="decimal/images/decimals_multiplication_0302_various_various_001_300.1675735237.jpg" alt="Multiplying 3-Digit by 2-Digit Numbers with Various Decimal Places" loading="lazy" width="250" height="324"><figcaption>Multiplying 3-Digit by 2-Digit Numbers with Various Decimal Places (<strong>1852 views this week</strong>)</figcaption></figure></a>
<a href="decimal/decround_various_various_001.html" title="Rounding Various Decimals to Various Decimal Places"><figure><img src="decimal/images/decround_various_various_001_300.1417828262.jpg" alt="Rounding Various Decimals to Various Decimal Places" loading="lazy" width="250" height="324"><figcaption>Rounding Various Decimals to Various Decimal Places (<strong>1737 views this week</strong>)</figcaption></figure></a>
<a href="decimal/decaddsubmixed13_001.html" title="Adding and Subtracting Decimals With Up to Three Places Before and After the Decimal"><figure><img src="decimal/images/decaddsubmixed13_001_300.1460561362.jpg" alt="Adding and Subtracting Decimals With Up to Three Places Before and After the Decimal" loading="lazy" width="250" height="324"><figcaption>Adding and Subtracting Decimals With Up to Three Places Before and After the Decimal (<strong>1296 views this week</strong>)</figcaption></figure></a>
<a href="decimal/decimals_division_tenths_001.html" title="Dividing Decimals by 1-Digit Tenths"><figure><img src="decimal/images/decimals_division_tenths_001_300.1417370367.jpg" alt="Dividing Decimals by 1-Digit Tenths" loading="lazy" width="250" height="324"><figcaption>Dividing Decimals by 1-Digit Tenths (<strong>694 views this week</strong>)</figcaption></figure></a>
<a href="decimal/decaddsubmixed12_001.html" title="Adding and Subtracting Decimals With Up to Two Places Before and After the Decimal"><figure><img src="decimal/images/decaddsubmixed12_001_300.1460561374.jpg" alt="Adding and Subtracting Decimals With Up to Two Places Before and After the Decimal" loading="lazy" width="250" height="324"><figcaption>Adding and Subtracting Decimals With Up to Two Places Before and After the Decimal (<strong>647 views this week</strong>)</figcaption></figure></a>
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<h2 id="decimal-grids-charts">Grids and Charts Useful for Learning Decimals</h2>
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<li><p>General use decimal printables are used in a variety of contexts and assist students in completing math questions related to decimals.</p></li>
<li><p>The thousandths grid is a useful tool in representing decimals. Each small rectangle represents a thousandth. Each square represents a hundredth. Each row or column represents a tenth. The entire grid represents one whole. The hundredths grid can be used to model percents or decimals. The decimal place value chart is a tool used with students who are first learning place value related to decimals or for those students who have difficulty with place value when working with decimals.</p></li>
<li><input type="checkbox" class="list-checkbox" id="decimal-grids-charts-1"><label for="decimal-grids-charts-1" class="wtitle">Thousandths and Hundredths Grids</label>
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<a href="decimal/blmthousandthsgrid.html" class=""><strong>Thousandths</strong> Grid</a>
<a href="decimal/blmhundredthsgrid.html" class=""><strong>Hundredths</strong> Grids (<strong>4</strong> on a page)</a>
<a href="decimal/hundredths_grids_nine.html" class=""><strong>Hundredths</strong> Grids (<strong>9</strong> on a page)</a>
<a href="decimal/hundredths_grids_twenty.html" class=""><strong>Hundredths</strong> Grids (<strong>20</strong> on a page)</a>
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<li><input type="checkbox" class="list-checkbox" id="decimal-grids-charts-2"><label for="decimal-grids-charts-2" class="wtitle">Decimal Place Value Charts</label>
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<a href="placevalueworksheets/decimal_place_value_chart_ones_hundredths.html" class="">Decimal Place Value Chart (<strong>Ones to Hundredths</strong>)</a>
<a href="placevalueworksheets/decimal_place_value_chart_ones_thousandths.html" class="">Decimal Place Value Chart (<strong>Ones to Thousandths</strong>)</a>
<a href="placevalueworksheets/decimal_place_value_chart_hundreds_hundredths.html" class="">Decimal Place Value Chart (<strong>Hundreds to Hundredths</strong>)</a>
<a href="placevalueworksheets/decimal_place_value_chart_thousands_thousandths.html" class="">Decimal Place Value Chart (<strong>Thousands to Thousandths</strong>)</a>
<a href="placevalueworksheets/decimalplacevaluechart.html" class="">Decimal Place Value Chart (<strong>Hundred Thousands to Thousandths</strong>)</a>
<a href="placevalueworksheets/decimal_place_value_chart_hundredmillions_millionths.html" class="">Decimal Place Value Chart (<strong>Hundred Millions to Millionths</strong>)</a>
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<h2 id="decimals-expanded-form">Decimals in Expanded Form</h2>
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<div class="imagearea">
<img src="decimal/images/decimals_standard_to_expanded_factors_form_using_decimals_1_8_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
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<li><p>For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart, and allow them to use it when converting standard form numbers to expanded form. There are actually five ways (two more than with integers) to write expanded form for decimals, and which one you use depends on your application or preference. Here is a quick summary of the various ways using the decimal number 1.23.
<br>1. Expanded Form using decimals: 1 + 0.2 + 0.03
<br>2. Expanded Form using fractions: 1 + <sup>2</sup>⁄<sub>10</sub> + <sup>3</sup>⁄<sub>100</sub>
<br>3. Expanded Factors Form using decimals: (1 × 1) + (2 × 0.1) + (3 × 0.01)
<br>4. Expanded Factors Form using fractions: (1 × 1) + (2 × <sup>1</sup>⁄<sub>10</sub>) + (3 × <sup>1</sup>⁄<sub>100</sub>)
<br>5. Expanded Exponential Form: (1 × 10<sup>0</sup>) + (2 × 10<sup>-1</sup>) + (3 × 10<sup>-2</sup>)</p></li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-3"><label for="decimals-expanded-form-3" class="wtitle">Converting Decimals from Standard Form to Expanded Form Using Decimals</label>
<div class="desc">
<a href="decimal/decimals_standard_to_expanded_form_using_decimals_1_3_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Decimals</strong> (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_decimals_1_4_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Decimals</strong> (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_decimals_1_5_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Decimals</strong> (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_decimals_1_6_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Decimals</strong> (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_decimals_1_7_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Decimals</strong> (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_decimals_1_8_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Decimals</strong> (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_decimals_1_9_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Decimals</strong> (<strong>9</strong> Decimal Places)</a>
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<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-4"><label for="decimals-expanded-form-4" class="wtitle">Converting Decimals from Standard Form to Expanded Form Using Fractions</label>
<div class="desc">
<a href="decimal/decimals_standard_to_expanded_form_using_fractions_1_3_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Fractions</strong> (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_fractions_1_4_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Fractions</strong> (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_fractions_1_5_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Fractions</strong> (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_fractions_1_6_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Fractions</strong> (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_fractions_1_7_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Fractions</strong> (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_fractions_1_8_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Fractions</strong> (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_form_using_fractions_1_9_001.html" class="">Converting Decimals from Standard to <strong>Expanded Form Using Fractions</strong> (<strong>9</strong> Decimal Places)</a>
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<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-5"><label for="decimals-expanded-form-5" class="wtitle">Converting Decimals from Standard Form to Expanded Factors Form Using Decimals</label>
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<a href="decimal/decimals_standard_to_expanded_factors_form_using_decimals_1_3_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Decimals</strong> (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_decimals_1_4_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Decimals</strong> (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_decimals_1_5_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Decimals</strong> (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_decimals_1_6_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Decimals</strong> (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_decimals_1_7_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Decimals</strong> (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_decimals_1_8_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Decimals</strong> (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_decimals_1_9_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Decimals</strong> (<strong>9</strong> Decimal Places)</a>
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</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-6"><label for="decimals-expanded-form-6" class="wtitle">Converting Decimals from Standard Form to Expanded Factors Form Using Fractions</label>
<div class="desc">
<a href="decimal/decimals_standard_to_expanded_factors_form_using_fractions_1_3_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Fractions</strong> (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_fractions_1_4_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Fractions</strong> (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_fractions_1_5_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Fractions</strong> (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_fractions_1_6_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Fractions</strong> (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_fractions_1_7_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Fractions</strong> (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_fractions_1_8_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Fractions</strong> (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_factors_form_using_fractions_1_9_001.html" class="">Converting Decimals from Standard to <strong>Expanded Factors Form Using Fractions</strong> (<strong>9</strong> Decimal Places)</a>
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</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-7"><label for="decimals-expanded-form-7" class="wtitle">Converting Decimals from Standard Form to Expanded Exponential Form</label>
<div class="desc">
<a href="decimal/decimals_standard_to_expanded_exponential_form_1_3_001.html" class="">Converting Decimals from Standard to <strong>Expanded Exponential Form</strong> (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_exponential_form_1_4_001.html" class="">Converting Decimals from Standard to <strong>Expanded Exponential Form</strong> (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_exponential_form_1_5_001.html" class="">Converting Decimals from Standard to <strong>Expanded Exponential Form</strong> (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_exponential_form_1_6_001.html" class="">Converting Decimals from Standard to <strong>Expanded Exponential Form</strong> (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_exponential_form_1_7_001.html" class="">Converting Decimals from Standard to <strong>Expanded Exponential Form</strong> (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_exponential_form_1_8_001.html" class="">Converting Decimals from Standard to <strong>Expanded Exponential Form</strong> (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_standard_to_expanded_exponential_form_1_9_001.html" class="">Converting Decimals from Standard to <strong>Expanded Exponential Form</strong> (<strong>9</strong> Decimal Places)</a>
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<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-8"><label for="decimals-expanded-form-8" class="wtitle">Retro Converting Decimals from Standard Form to Expanded Form</label>
<div class="desc">
<a href="decimal/decimals_standard_to_expanded_form_3_2_001.html" class="">Retro Standard to Expanded Form (3 digits before decimal; 2 after)</a>
<a href="decimal/decimals_standard_to_expanded_form_4_3_001.html" class="">Retro Standard to Expanded Form (4 digits before decimal; 3 after)</a>
<a href="decimal/decimals_standard_to_expanded_form_6_4_001.html" class="">Retro Standard to Expanded Form (6 digits before decimal; 4 after)</a>
<a href="decimal/decimals_standard_to_expanded_form_12_3_001.html" class="">Retro Standard to Expanded Form (12 digits before decimal; 3 after)</a>
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</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-9"><label for="decimals-expanded-form-9" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> Retro European Format Converting Decimals from Standard Form to Expanded Form</label>
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<a href="decimal/euro_decimals_standard_to_expanded_form_3_2_001.html" class="">Standard to Expanded Form (3 digits before decimal; 2 after)</a>
<a href="decimal/euro_decimals_standard_to_expanded_form_4_3_001.html" class="">Standard to Expanded Form (4 digits before decimal; 3 after)</a>
<a href="decimal/euro_decimals_standard_to_expanded_form_6_4_001.html" class="">Standard to Expanded Form (6 digits before decimal; 4 after)</a>
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<li><p>Of course, being able to convert numbers already in expanded form to standard form is also important. All five versions of decimal expanded form are included in these worksheets.</p></li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-10"><label for="decimals-expanded-form-10" class="wtitle">Converting Decimals to Standard Form from Expanded Form Using Decimals</label>
<div class="desc">
<a href="decimal/decimals_expanded_form_to_standard_using_decimals_1_3_001.html" class="">Converting Decimals from <strong>Expanded Form Using Decimals</strong> to Standard Form (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_decimals_1_4_001.html" class="">Converting Decimals from <strong>Expanded Form Using Decimals</strong> to Standard Form (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_decimals_1_5_001.html" class="">Converting Decimals from <strong>Expanded Form Using Decimals</strong> to Standard Form (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_decimals_1_6_001.html" class="">Converting Decimals from <strong>Expanded Form Using Decimals</strong> to Standard Form (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_decimals_1_7_001.html" class="">Converting Decimals from <strong>Expanded Form Using Decimals</strong> to Standard Form (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_decimals_1_8_001.html" class="">Converting Decimals from <strong>Expanded Form Using Decimals</strong> to Standard Form (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_decimals_1_9_001.html" class="">Converting Decimals from <strong>Expanded Form Using Decimals</strong> to Standard Form (<strong>9</strong> Decimal Places)</a>
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</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-11"><label for="decimals-expanded-form-11" class="wtitle">Converting Decimals to Standard Form from Expanded Form Using Fractions</label>
<div class="desc">
<a href="decimal/decimals_expanded_form_to_standard_using_fractions_1_3_001.html" class="">Converting Decimals from <strong>Expanded Form Using Fractions</strong> to Standard Form (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_fractions_1_4_001.html" class="">Converting Decimals from <strong>Expanded Form Using Fractions</strong> to Standard Form (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_fractions_1_5_001.html" class="">Converting Decimals from <strong>Expanded Form Using Fractions</strong> to Standard Form (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_fractions_1_6_001.html" class="">Converting Decimals from <strong>Expanded Form Using Fractions</strong> to Standard Form (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_fractions_1_7_001.html" class="">Converting Decimals from <strong>Expanded Form Using Fractions</strong> to Standard Form (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_fractions_1_8_001.html" class="">Converting Decimals from <strong>Expanded Form Using Fractions</strong> to Standard Form (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_form_to_standard_using_fractions_1_9_001.html" class="">Converting Decimals from <strong>Expanded Form Using Fractions</strong> to Standard Form (<strong>9</strong> Decimal Places)</a>
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</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-12"><label for="decimals-expanded-form-12" class="wtitle">Converting Decimals to Standard Form from Expanded Factors Form Using Decimals</label>
<div class="desc">
<a href="decimal/decimals_expanded_factors_form_to_standard_using_decimals_1_3_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Decimals</strong> to Standard Form (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_decimals_1_4_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Decimals</strong> to Standard Form (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_decimals_1_5_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Decimals</strong> to Standard Form (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_decimals_1_6_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Decimals</strong> to Standard Form (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_decimals_1_7_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Decimals</strong> to Standard Form (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_decimals_1_8_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Decimals</strong> to Standard Form (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_decimals_1_9_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Decimals</strong> to Standard Form (<strong>9</strong> Decimal Places)</a>
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<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-13"><label for="decimals-expanded-form-13" class="wtitle">Converting Decimals to Standard Form from Expanded Factors Form Using Fractions</label>
<div class="desc">
<a href="decimal/decimals_expanded_factors_form_to_standard_using_fractions_1_3_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Fractions</strong> to Standard Form (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_fractions_1_4_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Fractions</strong> to Standard Form (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_fractions_1_5_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Fractions</strong> to Standard Form (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_fractions_1_6_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Fractions</strong> to Standard Form (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_fractions_1_7_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Fractions</strong> to Standard Form (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_fractions_1_8_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Fractions</strong> to Standard Form (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_factors_form_to_standard_using_fractions_1_9_001.html" class="">Converting Decimals from <strong>Expanded Factors Form Using Fractions</strong> to Standard Form (<strong>9</strong> Decimal Places)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-14"><label for="decimals-expanded-form-14" class="wtitle">Converting Decimals to Standard Form from Expanded Exponential Form</label>
<div class="desc">
<a href="decimal/decimals_expanded_exponential_form_to_standard_1_3_001.html" class="">Converting Decimals from <strong>Expanded Exponential Form</strong> to Standard Form (<strong>3</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_exponential_form_to_standard_1_4_001.html" class="">Converting Decimals from <strong>Expanded Exponential Form</strong> to Standard Form (<strong>4</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_exponential_form_to_standard_1_5_001.html" class="">Converting Decimals from <strong>Expanded Exponential Form</strong> to Standard Form (<strong>5</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_exponential_form_to_standard_1_6_001.html" class="">Converting Decimals from <strong>Expanded Exponential Form</strong> to Standard Form (<strong>6</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_exponential_form_to_standard_1_7_001.html" class="">Converting Decimals from <strong>Expanded Exponential Form</strong> to Standard Form (<strong>7</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_exponential_form_to_standard_1_8_001.html" class="">Converting Decimals from <strong>Expanded Exponential Form</strong> to Standard Form (<strong>8</strong> Decimal Places)</a>
<a href="decimal/decimals_expanded_exponential_form_to_standard_1_9_001.html" class="">Converting Decimals from <strong>Expanded Exponential Form</strong> to Standard Form (<strong>9</strong> Decimal Places)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-15"><label for="decimals-expanded-form-15" class="wtitle">Retro Converting Decimals to Standard Form from Expanded Form</label>
<div class="desc">
<a href="decimal/decimals_expanded_to_standard_form_3_2_001.html" class="">Retro Expanded to Standard Form (3 digits before decimal; 2 after)</a>
<a href="decimal/decimals_expanded_to_standard_form_4_3_001.html" class="">Retro Expanded to Standard Form (4 digits before decimal; 3 after)</a>
<a href="decimal/decimals_expanded_to_standard_form_6_4_001.html" class="">Retro Expanded to Standard Form (6 digits before decimal; 4 after)</a>
<a href="decimal/decimals_expanded_to_standard_form_12_3_001.html" class="">Retro Expanded to Standard Form (12 digits before decimal; 3 after)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="decimals-expanded-form-16"><label for="decimals-expanded-form-16" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> Retro European Format Converting Decimals to Standard Form from Expanded Form</label>
<div class="desc">
<a href="decimal/euro_decimals_expanded_to_standard_form_3_2_001.html" class="">Retro European Format Expanded to Standard Form (3 digits before decimal; 2 after)</a>
<a href="decimal/euro_decimals_expanded_to_standard_form_4_3_001.html" class="">Retro European Format Expanded to Standard Form (4 digits before decimal; 3 after)</a>
<a href="decimal/euro_decimals_expanded_to_standard_form_6_4_001.html" class="">Retro European Format Expanded to Standard Form (6 digits before decimal; 4 after)</a>
</div>
</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="rounding-decimals">Rounding Decimals Worksheets</h2>
</div>
<div class="imagearea">
<img src="decimal/images/decround_10_whole_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>Rounding decimals is similar to rounding whole numbers; you have to know your place value! When learning about rounding, it is also useful to learn about truncating since it may help students to round properly. A simple strategy for rounding involves truncating, using the digits after the truncation to determine whether the new terminating digit remains the same or gets incremented, then taking action by incrementing if necessary and throwing away the rest. Here is a simple example: Round 4.567 to the nearest tenth. First, truncate the number after the tenths place 4.5|67. Next, look at the truncated part (67). Is it more than half way to 99 (i.e. 50 or more)? It is, so the decision will be to increment. Lastly, increment the tenths value by 1 to get 4.6. Of course, the situation gets a little more complicated if the terminating digit is a 9. In that case, some regrouping might be necessary. For example: Round 6.959 to the nearest tenth. Truncate: 6.9|59. Decide to increment since 59 is more than half way to 99. Incrementing results in the necessity to regroup the tenths into an extra one whole, so the result is 7.0. Watch that students do not write 6.10. You will want to correct them right away in that case. One last note: if there are three truncated digits then the question becomes is the number more than half way to 999. Likewise, for one digit; is the number more than half way to 9. And so on...</p></li>
<li><p>We should also mention that in some scientific and mathematical "circles," rounding is slightly different "on a 5". For example, most people would round up on a 5 such as: 6.5 --> 7; 3.555 --> 3.56; 0.60500 --> 0.61; etc. A different way to round on a 5, however, is to round to the nearest even number, so 5.5 would be rounded up to 6, but 8.5 would be rounded down to 8. The main reason for this is not to skew the results of a large number of rounding events. If you always round up on a 5, on average, you will have slightly higher results than you should. Because most pre-college students round up on a 5, that is what we have done in the worksheets that follow.</p></li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-17"><label for="rounding-decimals-17" class="wtitle">Rounding Decimals to Whole Numbers</label>
<div class="desc">
<a href="decimal/decround_10_whole_001.html" class="">Round <strong>Tenths</strong> to a <strong>Whole</strong> Number</a>
<a href="decimal/decround_100_whole_001.html" class="">Round <strong>Hundredths</strong> to a <strong>Whole</strong> Number</a>
<a href="decimal/decround_1000_whole_001.html" class="">Round <strong>Thousandths</strong> to a <strong>Whole</strong> Number</a>
<a href="decimal/decround_10000_whole_001.html" class="">Round <strong>Ten Thousandths</strong> to a <strong>Whole</strong> Number</a>
<a href="decimal/decround_various_whole_001.html" class="">Round <strong>Various</strong> Decimals to a <strong>Whole</strong> Number</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-18"><label for="rounding-decimals-18" class="wtitle">Rounding Decimals to Tenths</label>
<div class="desc">
<a href="decimal/decround_100_10_001.html" class="">Round <strong>Hundredths</strong> to <strong>Tenths</strong></a>
<a href="decimal/decround_1000_10_001.html" class="">Round <strong>Thousandths</strong> to <strong>Tenths</strong></a>
<a href="decimal/decround_10000_10_001.html" class="">Round <strong>Ten Thousandths</strong> to <strong>Tenths</strong></a>
<a href="decimal/decround_various_10_001.html" class="">Round <strong>Various</strong> Decimals to <strong>Tenths</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-19"><label for="rounding-decimals-19" class="wtitle">Rounding Decimals to Hundredths</label>
<div class="desc">
<a href="decimal/decround_1000_100_001.html" class="">Round <strong>Thousandths</strong> to <strong>Hundredths</strong></a>
<a href="decimal/decround_10000_100_001.html" class="">Round <strong>Ten Thousandths</strong> to <strong>Hundredths</strong></a>
<a href="decimal/decround_various_100_001.html" class="">Round <strong>Various</strong> Decimals to <strong>Hundredths</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-20"><label for="rounding-decimals-20" class="wtitle">Rounding Decimals to Thousandths</label>
<div class="desc">
<a href="decimal/decround_10000_1000_001.html" class="">Round <strong>Ten Thousandths</strong> to <strong>Thousandths</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-21"><label for="rounding-decimals-21" class="wtitle">Rounding Decimals to Various Decimal Places</label>
<div class="desc">
<a href="decimal/decround_100_various_001.html" class="">Round <strong>Hundredths</strong> to <strong>Various</strong> Decimal Places</a>
<a href="decimal/decround_1000_various_001.html" class="">Round <strong>Thousandths</strong> to <strong>Various</strong> Decimal Places</a>
<a href="decimal/decround_10000_various_001.html" class="">Round <strong>Ten Thousandths</strong> to <strong>Various</strong> Decimal Places</a>
<a href="decimal/decround_various_various_001.html" class="">Round <strong>Various</strong> Decimals to <strong>Various</strong> Decimal Places</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-22"><label for="rounding-decimals-22" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Rounding Decimals to Whole Numbers</label>
<div class="desc">
<a href="decimal/euro_decimals_rounding_tenth_to_whole_001.html" class="">European Format Round Tenths to a Whole Number</a>
<a href="decimal/euro_decimals_rounding_hundredth_to_whole_001.html" class="">European Format Round Hundredths to a Whole Number</a>
<a href="decimal/euro_decimals_rounding_thousandth_to_whole_001.html" class="">European Format Round Thousandths to a Whole Number</a>
<a href="decimal/euro_decimals_rounding_tenthousandth_to_whole_001.html" class="">European Format Round Ten Thousandths to Whole Number</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-23"><label for="rounding-decimals-23" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Rounding Decimals to Tenths</label>
<div class="desc">
<a href="decimal/euro_decimals_rounding_hundredth_to_tenth_001.html" class="">European Format Round Hundredths to Tenths</a>
<a href="decimal/euro_decimals_rounding_thousandth_to_tenth_001.html" class="">European Format Round Thousandths to Tenths</a>
<a href="decimal/euro_decimals_rounding_tenthousandth_to_tenth_001.html" class="">European Format Round Ten Thousandths to Tenths</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-24"><label for="rounding-decimals-24" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Rounding Decimals to Hundredths</label>
<div class="desc">
<a href="decimal/euro_decimals_rounding_thousandth_to_hundredth_001.html" class="">European Format Round Thousandths to Hundredths</a>
<a href="decimal/euro_decimals_rounding_tenthousandth_to_hundredth_001.html" class="">European Format Round Ten Thousandths to Hundredths</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="rounding-decimals-25"><label for="rounding-decimals-25" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Rounding Decimals to Thousandths</label>
<div class="desc">
<a href="decimal/euro_decimals_rounding_tenthousandth_to_thousandth_001.html" class="">European Format Round Ten Thousandths to Thousandths</a>
</div>
</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="comparing-ordering-decimals">Comparing and Ordering/Sorting Decimals Worksheets.</h2>
</div>
<div class="imagearea">
<img src="decimal/images/comparing_decimals_tenths_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>The comparing decimals worksheets have students compare pairs of numbers and the ordering decimals worksheets have students compare a list of numbers by sorting them.</p></li>
<li><p>Students who have mastered comparing whole numbers should find comparing decimals to be fairly easy. The easiest strategy is to compare the numbers before the decimal (the whole number part) first and only compare the decimal parts if the whole number parts are equal. These sorts of questions allow teachers/parents to get a good idea of whether students have grasped the concept of decimals or not. For example, if a student thinks that 4.93 is greater than 8.7, then they might need a little more instruction in place value. Close numbers means that some care was taken to make the numbers look similar. For example, they could be close in value, e.g. 3.3. and 3.4 or one of the digits might be changed as in 5.86 and 6.86.</p></li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-26"><label for="comparing-ordering-decimals-26" class="wtitle">Comparing Decimals up to Tenths</label>
<div class="desc">
<a href="decimal/comparing_decimals_tenths_001.html" class="">Comparing Decimals up to <strong>Tenths</strong> (<strong>Both Numbers Random</strong>)</a>
<a href="decimal/comparing_decimals_tenths_differs_001.html" class="">Comparing Decimals up to <strong>Tenths</strong> (<strong>One Digit Differs</strong>)</a>
<a href="decimal/comparing_decimals_tenths_tight_001.html" class="">Comparing Decimals up to <strong>Tenths</strong> (<strong>Both Numbers Close in Value</strong>)</a>
<a href="decimal/comparing_decimals_tenths_various_001.html" class="">Comparing Decimals up to <strong>Tenths</strong> (<strong>Various Tricks</strong>)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-27"><label for="comparing-ordering-decimals-27" class="wtitle">Comparing Decimals up to Hundredths</label>
<div class="desc">
<a href="decimal/comparing_decimals_hundredths_001.html" class="">Comparing Decimals up to <strong>Hundredths</strong> (<strong>Both Numbers Random</strong>)</a>
<a href="decimal/comparing_decimals_hundredths_differs_001.html" class="">Comparing Decimals up to <strong>Hundredths</strong> (<strong>One Digit Differs</strong>)</a>
<a href="decimal/comparing_decimals_hundredths_swapped_001.html" class="">Comparing Decimals up to <strong>Hundredths</strong> (<strong>Two Digits Swapped</strong>)</a>
<a href="decimal/comparing_decimals_hundredths_tight_001.html" class="">Comparing Decimals up to <strong>Hundredths</strong> (<strong>Both Numbers Close in Value</strong>)</a>
<a href="decimal/comparing_decimals_hundredths_extra_001.html" class="">Comparing Decimals up to <strong>Hundredths</strong> (<strong>One Number has an Extra Digit</strong>)</a>
<a href="decimal/comparing_decimals_hundredths_various_001.html" class="">Comparing Decimals up to <strong>Hundredths</strong> (<strong>Various Tricks</strong>)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-28"><label for="comparing-ordering-decimals-28" class="wtitle">Comparing Decimals up to Thousandths</label>
<div class="desc">
<a href="decimal/comparing_decimals_thousandths_001.html" class="">Comparing Decimals up to <strong>Thousandths</strong></a>
<a href="decimal/comparing_decimals_thousandths_differs_001.html" class="">Comparing Decimals up to <strong>Thousandths</strong> (<strong>One Digit Differs</strong>)</a>
<a href="decimal/comparing_decimals_thousandths_swapped_001.html" class="">Comparing Decimals up to <strong>Thousandths</strong> (<strong>Two Digits Swapped</strong>)</a>
<a href="decimal/comparing_decimals_thousandths_tight_001.html" class="">Comparing Decimals up to <strong>Thousandths</strong> (<strong>Both Numbers Close in Value</strong>)</a>
<a href="decimal/comparing_decimals_thousandths_extra_001.html" class="">Comparing Decimals up to <strong>Thousandths</strong> (<strong>One Number has an Extra Digit</strong>)</a>
<a href="decimal/comparing_decimals_thousandths_various_001.html" class="">Comparing Decimals up to <strong>Thousandths</strong> (<strong>Various Tricks</strong>)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-29"><label for="comparing-ordering-decimals-29" class="wtitle">Comparing Decimals up to Ten Thousandths</label>
<div class="desc">
<a href="decimal/comparing_decimals_tenthousandths_001.html" class="">Comparing Decimals up to <strong>Ten Thousandths</strong></a>
<a href="decimal/comparing_decimals_tenthousandths_differs_001.html" class="">Comparing Decimals up to <strong>Ten Thousandths</strong> (<strong>One Digit Differs</strong>)</a>
<a href="decimal/comparing_decimals_tenthousandths_swapped_001.html" class="">Comparing Decimals up to <strong>Ten Thousandths</strong> (<strong>Two Digits Swapped</strong>)</a>
<a href="decimal/comparing_decimals_tenthousandths_tight_001.html" class="">Comparing Decimals up to <strong>Ten Thousandths</strong> (<strong>Both Numbers Close in Value</strong>)</a>
<a href="decimal/comparing_decimals_tenthousandths_extra_001.html" class="">Comparing Decimals up to <strong>Ten Thousandths</strong> (<strong>One Number has an Extra Digit</strong>)</a>
<a href="decimal/comparing_decimals_tenthousandths_various_001.html" class="">Comparing Decimals up to <strong>Ten Thousandths</strong> (<strong>Various Tricks</strong>)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-30"><label for="comparing-ordering-decimals-30" class="wtitle">Comparing Decimals up to Hundred Thousandths</label>
<div class="desc">
<a href="decimal/comparing_decimals_hundredthousandths_001.html" class="">Comparing Decimals up to <strong>Hundred Thousandths</strong></a>
<a href="decimal/comparing_decimals_hundredthousandths_differs_001.html" class="">Comparing Decimals up to <strong>Hundred Thousandths</strong> (<strong>One Digit Differs</strong>)</a>
<a href="decimal/comparing_decimals_hundredthousandths_swapped_001.html" class="">Comparing Decimals up to <strong>Hundred Thousandths</strong> (<strong>Two Digits Swapped</strong>)</a>
<a href="decimal/comparing_decimals_hundredthousandths_tight_001.html" class="">Comparing Decimals up to <strong>Hundred Thousandths</strong> (<strong>Both Numbers Close in Value</strong>)</a>
<a href="decimal/comparing_decimals_hundredthousandths_extra_001.html" class="">Comparing Decimals up to <strong>Hundred Thousandths</strong> (<strong>One Number has an Extra Digit</strong>)</a>
<a href="decimal/comparing_decimals_hundredthousandths_various_001.html" class="">Comparing Decimals up to <strong>Hundred Thousandths</strong> (<strong>Various Tricks</strong>)</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-31"><label for="comparing-ordering-decimals-31" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Comparing Decimals</label>
<div class="desc">
<a href="decimal/euro_comparing_decimals_tenths_001.html" class="">European Format Comparing Decimals up to Tenths</a>
<a href="decimal/euro_comparing_decimals_tenths_tight_001.html" class="">European Format Comparing Decimals up to Tenths (tight)</a>
<a href="decimal/euro_comparing_decimals_hundredths_001.html" class="">European Format Comparing Decimals up to Hundredths</a>
<a href="decimal/euro_comparing_decimals_hundredths_tight_001.html" class="">European Format Comparing Decimals up to Hundredths (tight)</a>
<a href="decimal/euro_comparing_decimals_thousandths_001.html" class="">European Format Comparing Decimals up to Thousandths</a>
<a href="decimal/euro_comparing_decimals_thousandths_tight_001.html" class="">European Format Comparing Decimals up to Thousandths (tight)</a>
</div>
</li>
<li><p>Ordering decimals is very much like comparing decimals except there are more than two numbers. Generally, students determine the least (or greatest) decimal to start, cross it off the list then repeat the process to find the next lowest/greatest until they get to the last number. Checking the list at the end is always a good idea.</p></li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-32"><label for="comparing-ordering-decimals-32" class="wtitle">Ordering/Sorting Decimals</label>
<div class="desc">
<a href="decimal/decimals_ordering_hundredths_001.html" class="">Ordering/Sorting Decimal Hundredths</a>
<a href="decimal/decimals_ordering_thousandths_001.html" class="">Ordering/Sorting Decimal Thousandths</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="comparing-ordering-decimals-33"><label for="comparing-ordering-decimals-33" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Ordering/Sorting Decimals</label>
<div class="desc">
<a href="decimal/euro_decimals_ordering_tenths_8_001.html" class="">European Format Ordering/Sorting Decimal Tenths (8 per set)</a>
<a href="decimal/euro_decimals_ordering_hundredths_8_001.html" class="">European Format Ordering/Sorting Decimal Hundredths (8 per set)</a>
<a href="decimal/euro_decimals_ordering_thousandths_8_001.html" class="">European Format Ordering/Sorting Decimal Thousandths (8 per set)</a>
<a href="decimal/euro_decimals_ordering_tenthousandths_8_001.html" class="">European Format Ordering/Sorting Decimal Ten Thousandths (8 per set)</a>
<a href="decimal/euro_decimals_ordering_various_8_001.html" class="">European Format Ordering/Sorting Decimals with Various Decimal Places(8 per set)</a>
</div>
</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="converting-decimals">Converting Decimals to Fractions and Other Number Formats</h2>
</div>
<div class="imagearea">
<img src="decimal/images/common_fractions_convert_to_decimal_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>There are many good reasons for converting decimals to other number formats. Dealing with a fraction in arithmetic is often easier than the equivalent decimal. Consider 0.333... which is equivalent to 1/3. Multiplying 300 by 0.333... is difficult, but multiplying 300 by 1/3 is super easy! Students should be familiar with some of the more common fraction/decimal conversions, so they can switch back and forth as needed.</p></li>
<li><input type="checkbox" class="list-checkbox" id="converting-decimals-34"><label for="converting-decimals-34" class="wtitle">Converting Between Decimals and Fractions</label>
<div class="desc">
<a href="decimal/common_fractions_convert_to_decimal_001.html" class="">Converting Fractions to Terminating Decimals</a>
<a href="decimal/fractions_convert_to_decimal_001.html" class="">Converting Fractions to Terminating and Repeating Decimals</a>
<a href="decimal/decimals_convert_terminating_only_decimals_to_fractions_001.html" class="">Converting Terminating Decimals to Fractions</a>
<a href="decimal/decimals_convert_to_fractions_001.html" class="">Converting Terminating and Repeating Decimals to Fractions</a>
<a href="decimal/convert_fractions_to_hundredths_001.html" class="">Converting Fractions to Hundredths</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="converting-decimals-35"><label for="converting-decimals-35" class="wtitle">Converting Between Decimals, Fraction, Percents and Ratios</label>
<div class="desc">
<a href="decimal/convert_fractions_no711_from_fractions_to_decimals_percents_ppratios_001.html" class=""><strong>Converting Fractions</strong> to Decimals, Percents and Part-to-Part Ratios</a>
<a href="decimal/convert_fractions_no711_from_fractions_to_decimals_percents_pwratios_001.html" class=""><strong>Converting Fractions</strong> to Decimals, Percents and Part-to-Whole Ratios</a>
<a href="decimal/convert_fractions_no711_from_decimals_to_fractions_percents_ppratios_001.html" class=""><strong>Converting Decimals</strong> to Fractions, Percents and Part-to-Part Ratios</a>
<a href="decimal/convert_fractions_no711_from_decimals_to_fractions_percents_pwratios_001.html" class=""><strong>Converting Decimals</strong> to Fractions, Percents and Part-to-Whole Ratios</a>
<a href="decimal/convert_fractions_no711_from_percents_to_fractions_decimals_ppratios_001.html" class=""><strong>Converting Percents</strong> to Fractions, Decimals and Part-to-Part Ratios</a>
<a href="decimal/convert_fractions_no711_from_percents_to_fractions_decimals_pwratios_001.html" class=""><strong>Converting Percents</strong> to Fractions, Decimals and Part-to-Whole Ratios</a>
<a href="decimal/convert_fractions_no711_from_ppratios_to_fractions_decimals_percents_001.html" class=""><strong>Converting Part-to-Part Ratios</strong> to Fractions, Decimals and Percents</a>
<a href="decimal/convert_fractions_no711_from_pwratios_to_fractions_decimals_percents_001.html" class=""><strong>Converting Part-to-Whole Ratios</strong> to Fractions, Decimals and Percents</a>
<a href="decimal/convert_fractions_no711_from_various_to_various_ppratios_001.html" class=""><strong>Converting Various</strong> Fractions, Decimals, Percents and Part-to-Part Ratios</a>
<a href="decimal/convert_fractions_no711_from_various_to_various_pwratios_001.html" class=""><strong>Converting Various</strong> Fractions, Decimals, Percents and Part-to-Whole Ratios</a>
<a href="decimal/convert_fractions_711_from_various_to_various_ppratios_001.html" class=""><strong>Converting Various</strong> Fractions, Decimals, Percents and Part-to-Part Ratios with 7ths and 11ths</a>
<a href="decimal/convert_fractions_711_from_various_to_various_pwratios_001.html" class=""><strong>Converting Various</strong> Fractions, Decimals, Percents and Part-to-Whole Ratios with 7ths and 11ths</a>
</div>
</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="adding-subtracting-decimals">Adding and Subtracting Decimals</h2>
</div>
<div class="imagearea">
<img src="decimal/images/decimals_addition_tenths_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>Try the following mental addition strategy for decimals. Begin by ignoring the decimals in the addition question. Add the numbers as if they were whole numbers. For example, 3.25 + 4.98 could be viewed as 325 + 498 = 823. Use an estimate to decide where to place the decimal. In the example, 3.25 + 4.98 is approximately 3 + 5 = 8, so the decimal in the sum must go between the 8 and the 2 (i.e. 8.23)</p></li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-36"><label for="adding-subtracting-decimals-36" class="wtitle">Adding Tenths</label>
<div class="desc">
<a href="decimal/decimals_addition_tenths_001.html" class="">Adding Decimal <strong>Tenths</strong> with 0 Before the Decimal <strong>(range 0.1 to 0.9)</strong></a>
<a href="decimal/decimals_addition_ones_tenths_001.html" class="">Adding Decimal <strong>Tenths</strong> with 1 Digit Before the Decimal <strong>(range 1.1 to 9.9)</strong></a>
<a href="decimal/decimals_addition_tens_tenths_001.html" class="">Adding Decimal <strong>Tenths</strong> with 2 Digits Before the Decimal <strong>(range 10.1 to 99.9)</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-37"><label for="adding-subtracting-decimals-37" class="wtitle">Adding Hundredths</label>
<div class="desc">
<a href="decimal/decimals_addition_hundredths_001.html" class="">Adding Decimal <strong>Hundredths</strong> with 0 Before the Decimal <strong>(range 0.01 to 0.99)</strong></a>
<a href="decimal/decimals_addition_ones_hundredths_001.html" class="">Adding Decimal <strong>Hundredths</strong> with 1 Digit Before the Decimal <strong>(range 1.01 to 9.99)</strong></a>
<a href="decimal/decimals_addition_tens_hundredths_001.html" class="">Adding Decimal <strong>Hundredths</strong> with 2 Digits Before the Decimal <strong>(range 10.01 to 99.99)</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-38"><label for="adding-subtracting-decimals-38" class="wtitle">Adding Thousandths</label>
<div class="desc">
<a href="decimal/decimals_addition_thousandths_001.html" class="">Adding Decimal <strong>Thousandths</strong> with 0 Before the Decimal <strong>(range 0.001 to 0.999)</strong></a>
<a href="decimal/decimals_addition_ones_thousandths_001.html" class="">Adding Decimal <strong>Thousandths</strong> with 1 Digit Before the Decimal <strong>(range 1.001 to 9.999)</strong></a>
<a href="decimal/decimals_addition_tens_thousandths_001.html" class="">Adding Decimal <strong>Thousandths</strong> with 2 Digits Before the Decimal <strong>(range 10.001 to 99.999)</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-39"><label for="adding-subtracting-decimals-39" class="wtitle">Adding Ten Thousandths</label>
<div class="desc">
<a href="decimal/decimals_addition_tenthousandths_001.html" class="">Adding Decimal <strong>Ten Thousandths</strong> with 0 Before the Decimal <strong>(range 0.0001 to 0.9999)</strong></a>
<a href="decimal/decimals_addition_ones_tenthousandths_001.html" class="">Adding Decimal <strong>Ten Thousandths</strong> with 1 Digit Before the Decimal <strong>(range 1.0001 to 9.9999)</strong></a>
<a href="decimal/decimals_addition_tens_tenthousandths_001.html" class="">Adding Decimal <strong>Ten Thousandths</strong> with 2 Digits Before the Decimal <strong>(range 10.0001 to 99.9999)</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-40"><label for="adding-subtracting-decimals-40" class="wtitle">Adding Various Decimal Places</label>
<div class="desc">
<a href="decimal/decimals_addition_mixed_001.html" class="">Adding <strong>Various</strong> Decimal Places with 0 Before the Decimal</a>
<a href="decimal/decimals_addition_ones_mixed_001.html" class="">Adding <strong>Various</strong> Decimal Places with 1 Digit Before the Decimal</a>
<a href="decimal/decimals_addition_tens_mixed_001.html" class="">Adding <strong>Various</strong> Decimal Places with 2 Digits Before the Decimal</a>
<a href="decimal/decimals_addition_mixed_mixed_001.html" class="">Adding <strong>Various</strong> Decimal Places with Various Numbers of Digits Before the Decimal</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-41"><label for="adding-subtracting-decimals-41" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Adding Decimals</label>
<div class="desc">
<a href="decimal/euro_decimals_addition_tenths_001.html" class="">European Format Adding decimal tenths with 0 before the decimal (range 0,1 to 0,9)</a>
<a href="decimal/euro_decimals_addition_ones_tenths_001.html" class="">European Format Adding decimal tenths with 1 digit before the decimal (range 1,1 to 9,9)</a>
<a href="decimal/euro_decimals_addition_hundredths_001.html" class="">European Format Adding decimal hundredths with 0 before the decimal (range 0,01 to 0,99)</a>
<a href="decimal/euro_decimals_addition_ones_hundredths_001.html" class="">European Format Adding decimal hundredths with 1 digit before the decimal (range 1,01 to 9,99)</a>
<a href="decimal/euro_decimals_addition_thousandths_001.html" class="">European Format Adding decimal thousandths with 0 before the decimal (range 0,001 to 0,999)</a>
<a href="decimal/euro_decimals_addition_ones_thousandths_001.html" class="">European Format Adding decimal thousandths with 1 digit before the decimal (range 1,001 to 9,999)</a>
<a href="decimal/euro_decimals_addition_tenthousandths_001.html" class="">European Format Adding decimal ten thousandths with 0 before the decimal (range 0,0001 to 0,9999)</a>
<a href="decimal/euro_decimals_addition_ones_tenthousandths_001.html" class="">European Format Adding decimal ten thousandths with 1 digit before the decimal (range 1,0001 to 9,9999)</a>
<a href="decimal/euro_decimals_addition_various_001.html" class="">European Format Adding mixed decimals with Various Decimal Places</a>
<a href="decimal/euro_decimals_addition_ones_various_001.html" class="">European Format Adding mixed decimals with Various Decimal Places (1 to 9 before decimal)</a>
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</li>
<li><p>Base ten blocks can be used for decimal subtraction. Just redefine the blocks, so the big block is a one, the flat is a tenth, the rod is a hundredth and the little cube is a thousandth. Model and subtract decimals using base ten blocks, so students can "see" how decimals really work.</p></li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-42"><label for="adding-subtracting-decimals-42" class="wtitle">Subtracting Tenths</label>
<div class="desc">
<a href="decimal/decimals_subtraction_tenths_001.html" class="">Subtracting Decimal <strong>Tenths</strong> with <strong>No Integer Part</strong></a>
<a href="decimal/decimals_subtraction_ones_tenths_easy_001.html" class="">Subtracting Decimal <strong>Tenths</strong> with an <strong>Integer Part in the Minuend</strong></a>
<a href="decimal/decimals_subtraction_ones_tenths_001.html" class="">Subtracting Decimal <strong>Tenths</strong> with an <strong>Integer Part in the Minuend and Subtrahend</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-43"><label for="adding-subtracting-decimals-43" class="wtitle">Subtracting Hundredths</label>
<div class="desc">
<a href="decimal/decimals_subtraction_hundredths_001.html" class="">Subtracting Decimal <strong>Hundredths</strong> with <strong>No Integer Part</strong></a>
<a href="decimal/decimals_subtraction_ones_hundredths_easy_001.html" class="">Subtracting Decimal <strong>Hundredths</strong> with an <strong>Integer Part in the Minuend and Subtrahend</strong></a>
<a href="decimal/decimals_subtraction_ones_hundredths_001.html" class="">Subtracting Decimal <strong>Hundredths</strong> with a <strong>Larger Integer Part in the Minuend</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-44"><label for="adding-subtracting-decimals-44" class="wtitle">Subtracting Thousandths</label>
<div class="desc">
<a href="decimal/decimals_subtraction_thousandths_001.html" class="">Subtracting Decimal <strong>Thousandths</strong> with <strong>No Integer Part</strong></a>
<a href="decimal/decimals_subtraction_thousandths_integer_part_001.html" class="">Subtracting Decimal <strong>Thousandths</strong> with an <strong>Integer Part in the Minuend and Subtrahend</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-45"><label for="adding-subtracting-decimals-45" class="wtitle">Subtracting Ten Thousandths</label>
<div class="desc">
<a href="decimal/decimals_subtraction_tenthousandths_001.html" class="">Subtracting Decimal <strong>Ten Thousandths</strong> with <strong>No Integer Part</strong></a>
<a href="decimal/decimals_subtraction_tenthousandths_integer_part_001.html" class="">Subtracting Decimal <strong>Ten Thousandths</strong> with an <strong>Integer Part in the Minuend and Subtrahend</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-46"><label for="adding-subtracting-decimals-46" class="wtitle">Subtracting Various Decimal Places</label>
<div class="desc">
<a href="decimal/decimals_subtraction_various_to_hundredths_001.html" class="">Subtracting <strong>Various Decimals to Hundredths</strong></a>
<a href="decimal/decimals_subtraction_various_to_thousandths_001.html" class="">Subtracting <strong>Various Decimals to Thousandths</strong></a>
<a href="decimal/decimals_subtraction_various_to_tenthousandths_001.html" class="">Subtracting <strong>Various Decimals to Ten Thousandths</strong></a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-47"><label for="adding-subtracting-decimals-47" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Subtracting Decimals</label>
<div class="desc">
<a href="decimal/euro_decimals_subtraction_tenths_001.html" class="">European Format Decimal subtraction (range 0,1 to 0,9)</a>
<a href="decimal/euro_decimals_subtraction_ones_tenths_001.html" class="">European Format Decimal subtraction (range 1,1 to 9,9)</a>
<a href="decimal/euro_decimals_subtraction_hundredths_001.html" class="">European Format Decimal subtraction (range 0,01 to 0,99)</a>
<a href="decimal/euro_decimals_subtraction_ones_hundredths_001.html" class="">European Format Decimal subtraction (range 1,01 to 9,99)</a>
<a href="decimal/euro_decimals_subtraction_thousandths_001.html" class="">European Format Decimal subtraction (range 0,001 to 0,999)</a>
<a href="decimal/euro_decimals_subtraction_ones_thousandths_001.html" class="">European Format Decimal subtraction (range 1,001 to 9,999)</a>
<a href="decimal/euro_decimals_subtraction_tenthousandths_001.html" class="">European Format Decimal subtraction (range 0,0001 to 0,9999)</a>
<a href="decimal/euro_decimals_subtraction_ones_tenthousandths_001.html" class="">European Format Decimal subtraction (range 1,0001 to 9,9999)</a>
<a href="decimal/euro_decimals_subtraction_various_001.html" class="">European Format Decimal subtraction with Various Decimal Places</a>
<a href="decimal/euro_decimals_subtraction_ones_various_001.html" class="">European Format Decimal subtraction with Various Decimal Places (1 to 9 before decimal)</a>
</div>
</li>
<li><p>Adding and subtracting decimals is fairly straightforward when all the decimals are lined up. With the questions arranged horizontally, students are challenged to understand place value as it relates to decimals. A wonderful strategy for placing the decimal is to use estimation. For example if the question is 49.2 + 20.1, the answer without the decimal is 693. Estimate by rounding 49.2 to 50 and 20.1 to 20. 50 + 20 = 70. The decimal in 693 must be placed between the 9 and the 3 as in 69.3 to make the number close to the estimate of 70.</p></li>
<li><p>The above strategy will go a long way in students understanding operations with decimals, but it is also important that they have a strong foundation in place value and a proficiency with efficient strategies to be completely successful with these questions. As with any math skill, it is not wise to present this to students until they have the necessary prerequisite skills and knowledge.</p></li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-48"><label for="adding-subtracting-decimals-48" class="wtitle">Horizontally Arranged Adding Decimals</label>
<div class="desc">
<a href="decimal/decaddtenths_001.html" class=""><strong>Adding</strong> Decimals to <strong>Tenths</strong> Horizontally</a>
<a href="decimal/decaddhundredths_001.html" class=""><strong>Adding</strong> Decimals to <strong>Hundredths</strong> Horizontally</a>
<a href="decimal/decaddthousandths_001.html" class=""><strong>Adding</strong> Decimals to <strong>Thousandths</strong> Horizontally</a>
<a href="decimal/decaddtenthousandths_001.html" class=""><strong>Adding</strong> Decimals to <strong>Ten Thousandths</strong> Horizontally</a>
<a href="decimal/decaddmixed12_001.html" class=""><strong>Adding</strong> Decimals Horizontally With Up to <strong>Two Places</strong> Before and After the Decimal</a>
<a href="decimal/decaddmixed13_001.html" class=""><strong>Adding</strong> Decimals Horizontally With Up to <strong>Three Places</strong> Before and After the Decimal</a>
<a href="decimal/decaddmixed14_001.html" class=""><strong>Adding</strong> Decimals Horizontally With Up to <strong>Four Places</strong> Before and After the Decimal</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-49"><label for="adding-subtracting-decimals-49" class="wtitle">Horizontally Arranged Subtracting Decimals</label>
<div class="desc">
<a href="decimal/decsubtenths_001.html" class=""><strong>Subtracting</strong> Decimals to <strong>Tenths</strong> Horizontally</a>
<a href="decimal/decsubhundredths_001.html" class=""><strong>Subtracting</strong> Decimals to <strong>Hundredths</strong> Horizontally</a>
<a href="decimal/decsubthousandths_001.html" class=""><strong>Subtracting</strong> Decimals to <strong>Thousandths</strong> Horizontally</a>
<a href="decimal/decsubtenthousandths_001.html" class=""><strong>Subtracting</strong> Decimals to <strong>Ten Thousandths</strong> Horizontally</a>
<a href="decimal/decsubmixed12_001.html" class=""><strong>Subtracting</strong> Decimals Horizontally With Up to <strong>Two Places</strong> Before and After the Decimal</a>
<a href="decimal/decsubmixed13_001.html" class=""><strong>Subtracting</strong> Decimals Horizontally With Up to <strong>Three Places</strong> Before and After the Decimal</a>
<a href="decimal/decsubmixed14_001.html" class=""><strong>Subtracting</strong> Decimals Horizontally With Up to <strong>Four Places</strong> Before and After the Decimal</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="adding-subtracting-decimals-50"><label for="adding-subtracting-decimals-50" class="wtitle">Horizontally Arranged Mixed Adding and Subtracting Decimals</label>
<div class="desc">
<a href="decimal/decaddsubtenths_001.html" class=""><strong>Adding and Subtracting</strong> Decimals to <strong>Tenths</strong> Horizontally</a>
<a href="decimal/decaddsubhundredths_001.html" class=""><strong>Adding and Subtracting</strong> Decimals to <strong>Hundredths</strong> Horizontally</a>
<a href="decimal/decaddsubthousandths_001.html" class=""><strong>Adding and Subtracting</strong> Decimals to <strong>Thousandths</strong> Horizontally</a>
<a href="decimal/decaddsubtenthousandths_001.html" class=""><strong>Adding and Subtracting</strong> Decimals to <strong>Ten Thousandths</strong> Horizontally</a>
<a href="decimal/decaddsubmixed12_001.html" class=""><strong>Adding and Subtracting</strong> Decimals Horizontally With Up to <strong>Two Places</strong> Before and After the Decimal</a>
<a href="decimal/decaddsubmixed13_001.html" class=""><strong>Adding and Subtracting</strong> Decimals Horizontally With Up to <strong>Three Places</strong> Before and After the Decimal</a>
<a href="decimal/decaddsubmixed14_001.html" class=""><strong>Adding and Subtracting</strong> Decimals Horizontally With Up to <strong>Four Places</strong> Before and After the Decimal</a>
</div>
</li>
</ul>
</div>
</div>
<div class="wscontainer bc01">
<div class="titlearea">
<h2 id="multiplying-dividing-decimals">Multiplying and Dividing Decimals</h2>
</div>
<div class="imagearea">
<img src="decimal/images/decimals_multiplication_0201_tenths_whole_001_300.004.jpg" alt="" width="250" height="324" loading="lazy">
</div>
<div class="worksheetsarea">
<ul class="list">
<li><p>Multiplying decimals by whole numbers is very much like multiplying whole numbers except there is a decimal to deal with. Although students might initially have trouble with it, through the power of rounding and estimating, they can generally get it quite quickly. Many teachers will tell students to ignore the decimal and multiply the numbers just like they would whole numbers. This is a good strategy to use. Figuring out where the decimal goes at the end can be accomplished by counting how many decimal places were in the original question and giving the answer that many decimal places. To better understand this method, students can round the two factors and multiply in their head to get an estimate then place the decimal based on their estimate. For example, multiplying 9.84 × 91, students could first round the numbers to 10 and 91 (keep 91 since multiplying by 10 is easy) then get an estimate of 910. Actually multiplying (ignoring the decimal) gets you 89544. To get that number close to 910, the decimal needs to go between the 5 and the 4, thus 895.44. Note that there are two decimal places in the factors and two decimal places in the answer, but estimating made it more understandable rather than just a method.</p></li>
<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-51"><label for="multiplying-dividing-decimals-51" class="wtitle">Multiplying Decimals by 1-Digit Whole Numbers</label>
<div class="desc">
<a href="decimal/decimals_multiplication_0201_tenths_whole_001.html" class="">Multiply <strong>2-digit tenths</strong> by <strong>1-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0201_hundredths_whole_001.html" class="">Multiply <strong>2-digit hundredths</strong> by <strong>1-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0201_thousandths_whole_001.html" class="">Multiply <strong>2-digit thousandths</strong> by <strong>1-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0301_tenths_whole_001.html" class="">Multiply <strong>3-digit tenths</strong> by <strong>1-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0301_hundredths_whole_001.html" class="">Multiply <strong>3-digit hundredths</strong> by <strong>1-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0301_thousandths_whole_001.html" class="">Multiply <strong>3-digit thousandths</strong> by <strong>1-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_xx01_various_whole_001.html" class="">Multiply <strong>various decimals</strong> by <strong>1-digit</strong> whole numbers</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-52"><label for="multiplying-dividing-decimals-52" class="wtitle">Multiplying Decimals by 2-Digit Whole Numbers</label>
<div class="desc">
<a href="decimal/decimals_multiplication_0202_tenths_whole_001.html" class="">Multiplying <strong>2-digit tenths</strong> by <strong>2-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0202_hundredths_whole_001.html" class="">Multiplying <strong>2-digit hundredths</strong> by <strong>2-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0302_tenths_whole_001.html" class="">Multiplying <strong>3-digit tenths</strong> by <strong>2-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0302_hundredths_whole_001.html" class="">Multiplying <strong>3-digit hundredths</strong> by <strong>2-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_0302_thousandths_whole_001.html" class="">Multiplying <strong>3-digit thousandths</strong> by <strong>2-digit</strong> whole numbers</a>
<a href="decimal/decimals_multiplication_xx02_various_whole_001.html" class="">Multiplying <strong>various decimals</strong> by <strong>2-digit</strong> whole numbers</a>
</div>
</li>
<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-53"><label for="multiplying-dividing-decimals-53" class="wtitle">Multiplying Decimals by Tenths</label>
<div class="desc">
<a href="decimal/decimals_multiplication_0202_whole_tenths_001.html" class="">Multiplying <strong>2-digit whole</strong> by 2-digit <strong>tenths</strong></a>
<a href="decimal/decimals_multiplication_0202_tenths_tenths_001.html" class="">Multiplying <strong>2-digit tenths</strong> by 2-digit <strong>tenths</strong></a>
<a href="decimal/decimals_multiplication_0202_hundredths_tenths_001.html" class="">Multiplying <strong>2-digit hundredths</strong> by 2-digit <strong>tenths</strong></a>
<a href="decimal/decimals_multiplication_0302_whole_tenths_001.html" class="">Multiplying <strong>3-digit whole</strong> by 2-digit <strong>tenths</strong></a>
<a href="decimal/decimals_multiplication_0302_tenths_tenths_001.html" class="">Multiplying <strong>3-digit tenths</strong> by 2-digit <strong>tenths</strong></a>
<a href="decimal/decimals_multiplication_0302_hundredths_tenths_001.html" class="">Multiplying <strong>3-digit hundredths</strong> by 2-digit <strong>tenths</strong></a>
<a href="decimal/decimals_multiplication_0302_thousandths_tenths_001.html" class="">Multiplying <strong>3-digit thousandths</strong> by 2-digit <strong>tenths</strong></a>
<a href="decimal/decimals_multiplication_xx02_various_tenths_001.html" class="">Multiplying <strong>various decimals</strong> by 2-digit <strong>tenths</strong></a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-54"><label for="multiplying-dividing-decimals-54" class="wtitle">Multiplying Decimals by Hundredths</label>
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<a href="decimal/decimals_multiplication_0202_whole_hundredths_001.html" class="">Multiplying <strong>2-digit whole</strong> by 2-digit <strong>hundredths</strong></a>
<a href="decimal/decimals_multiplication_0202_tenths_hundredths_001.html" class="">Multiplying <strong>2-digit tenths</strong> by 2-digit <strong>hundredths</strong></a>
<a href="decimal/decimals_multiplication_0202_hundredths_hundredths_001.html" class="">Multiplying <strong>2-digit hundredths</strong> by 2-digit <strong>hundredths</strong></a>
<a href="decimal/decimals_multiplication_0302_whole_hundredths_001.html" class="">Multiplying <strong>3-digit whole</strong> by 2-digit <strong>hundredths</strong></a>
<a href="decimal/decimals_multiplication_0302_tenths_hundredths_001.html" class="">Multiplying <strong>3-digit tenths</strong> by 2-digit <strong>hundredths</strong></a>
<a href="decimal/decimals_multiplication_0302_hundredths_hundredths_001.html" class="">Multiplying <strong>3-digit hundredths</strong> by 2-digit <strong>hundredths</strong></a>
<a href="decimal/decimals_multiplication_0302_thousandths_hundredths_001.html" class="">Multiplying <strong>3-digit thousandths</strong> by 2-digit <strong>hundredths</strong></a>
<a href="decimal/decimals_multiplication_xx02_various_hundredths_001.html" class="">Multiplying <strong>various decimals</strong> by 2-digit <strong>hundredths</strong></a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-55"><label for="multiplying-dividing-decimals-55" class="wtitle">Multiplying Decimals by Various Decimal Places</label>
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<a href="decimal/decimals_multiplication_0202_various_various_001.html" class="">Multiplying 2-digit by 2-digit numbers with <strong>various</strong> decimal places</a>
<a href="decimal/decimals_multiplication_0302_various_various_001.html" class="">Multiplying 3-digit by 2-digit numbers with <strong>various</strong> decimal places</a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-56"><label for="multiplying-dividing-decimals-56" class="wtitle">Decimal Long Multiplication in Various Ranges</label>
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<a href="decimal/decimals_multiplication_tenths_001.html" class="">Decimal Multiplication (range 0.1 to 0.9)</a>
<a href="decimal/decimals_multiplication_ones_tenths_001.html" class="">Decimal Multiplication (range 1.1 to 9.9)</a>
<a href="decimal/decimals_multiplication_tens_tenths_001.html" class="">Decimal Multiplication (range 10.1 to 99.9)</a>
<a href="decimal/decimals_multiplication_hundredths_001.html" class="">Decimal Multiplication (range 0.01 to 0.99)</a>
<a href="decimal/decimals_multiplication_ones_hundredths_001.html" class="">Decimal Multiplication (range 1.01 to 9.99)</a>
<a href="decimal/decimals_multiplication_tens_hundredths_001.html" class="">Decimal Multiplication (range 10.01 to 99.99)</a>
<a href="decimal/dec_randig_ranplc_001.html" class="">Random # Digits Random # Places</a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-57"><label for="multiplying-dividing-decimals-57" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Multiplying Decimals by 2-Digit Whole Numbers</label>
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<a href="decimal/decimals_euro_multiplication_0202_whole_hundredths_001.html" class="">European Format 2-digit whole × 2-digit hundredths </a>
<a href="decimal/decimals_euro_multiplication_0202_tenths_whole_001.html" class="">European Format 2-digit tenths × 2-digit whole </a>
<a href="decimal/decimals_euro_multiplication_0202_hundredths_whole_001.html" class="">European Format 2-digit hundredths × 2-digit whole </a>
<a href="decimal/decimals_euro_multiplication_0302_tenths_whole_001.html" class="">European Format 3-digit tenths × 2-digit whole </a>
<a href="decimal/decimals_euro_multiplication_0302_hundredths_whole_001.html" class="">European Format 3-digit hundredths × 2-digit whole </a>
<a href="decimal/decimals_euro_multiplication_0302_thousandths_whole_001.html" class="">European Format 3-digit thousandths × 2-digit whole </a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-58"><label for="multiplying-dividing-decimals-58" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Multiplying Decimals by 2-Digit Tenths</label>
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<a href="decimal/decimals_euro_multiplication_0202_whole_tenths_001.html" class="">European Format 2-digit whole × 2-digit tenths </a>
<a href="decimal/decimals_euro_multiplication_0202_tenths_tenths_001.html" class="">European Format 2-digit tenths × 2-digit tenths </a>
<a href="decimal/decimals_euro_multiplication_0202_hundredths_tenths_001.html" class="">European Format 2-digit hundredths × 2-digit tenths </a>
<a href="decimal/decimals_euro_multiplication_0302_whole_tenths_001.html" class="">European Format 3-digit whole × 2-digit tenths </a>
<a href="decimal/decimals_euro_multiplication_0302_tenths_tenths_001.html" class="">European Format 3-digit tenths × 2-digit tenths </a>
<a href="decimal/decimals_euro_multiplication_0302_hundredths_tenths_001.html" class="">European Format 3-digit hundredths × 2-digit tenths </a>
<a href="decimal/decimals_euro_multiplication_0302_thousandths_tenths_001.html" class="">European Format 3-digit thousandths × 2-digit tenths </a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-59"><label for="multiplying-dividing-decimals-59" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Multiplying Decimals by 2-Digit Hundredths</label>
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<a href="decimal/decimals_euro_multiplication_0202_tenths_hundredths_001.html" class="">European Format 2-digit tenths × 2-digit hundredths </a>
<a href="decimal/decimals_euro_multiplication_0202_hundredths_hundredths_001.html" class="">European Format 2-digit hundredths × 2-digit hundredths </a>
<a href="decimal/decimals_euro_multiplication_0302_whole_hundredths_001.html" class="">European Format 3-digit whole × 2-digit hundredths </a>
<a href="decimal/decimals_euro_multiplication_0302_tenths_hundredths_001.html" class="">European Format 3-digit tenths × 2-digit hundredths </a>
<a href="decimal/decimals_euro_multiplication_0302_hundredths_hundredths_001.html" class="">European Format 3-digit hundredths × 2-digit hundredths </a>
<a href="decimal/decimals_euro_multiplication_0302_thousandths_hundredths_001.html" class="">European Format 3-digit thousandths × 2-digit hundredths </a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-60"><label for="multiplying-dividing-decimals-60" class="wtitle"><svg class="size32"><use xlink:href="includes/symbol-defs.006.svg#flag-eu"></use></svg> European Format Multiplying Decimals by Various Decimal Places</label>
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<a href="decimal/decimals_euro_multiplication_0202_various_various_001.html" class="">European Format 2-digit × 2-digit with various decimal places </a>
<a href="decimal/decimals_euro_multiplication_0302_various_various_001.html" class="">European Format 3-digit × 2-digit with various decimal places </a>
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<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-61"><label for="multiplying-dividing-decimals-61" class="wtitle">Dividing Decimals by Whole Numbers</label>
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<a href="decimal/decimals_division_tenth_by_whole_001.html" class="">Divide Tenths by a Whole Number</a>
<a href="decimal/decimals_division_hundredth_by_whole_001.html" class="">Divide Hundredths by a Whole Number</a>
<a href="decimal/decimals_division_thousandth_by_whole_001.html" class="">Divide Thousandths by a Whole Number</a>
<a href="decimal/decimals_division_tenthousandth_by_whole_001.html" class="">Divide Ten Thousandths by a Whole Number</a>
<a href="decimal/decimals_division_various_by_whole_001.html" class="">Divide Various Decimals by a Whole Number</a>
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<li><p>In case you aren't familiar with dividing with a decimal divisor, the general method for completing questions is by getting rid of the decimal in the divisor. This is done by multiplying the divisor and the dividend by the same amount, usually a power of ten such as 10, 100 or 1000. For example, if the division question is 5.32/5.6, you would multiply the divisor and dividend by 10 to get the equivalent division problem, 53.2/56. Completing this division will result in the exact same quotient as the original (try it on your calculator if you don't believe us). The main reason for completing decimal division in this way is to get the decimal in the correct location when using the U.S. long division algorithm.</p></li>
<li><p>A much simpler strategy, in our opinion, is to initially ignore the decimals all together and use estimation to place the decimal in the quotient. In the same example as above, you would complete 532/56 = 95. If you "flexibly" round the original, you will get about 5/5 which is about 1, so the decimal in 95 must be placed to make 95 close to 1. In this case, you would place it just before the 9 to get 0.95. Combining this strategy with the one above can also help a great deal with more difficult questions. For example, 4.584184 ÷ 0.461 can first be converted the to equivalent: 4584.184 ÷ 461 (you can estimate the quotient to be around 10). Complete the division question without decimals: 4584184 ÷ 461 = 9944 then place the decimal, so that 9944 is about 10. This results in 9.944.</p></li>
<li><p>Dividing decimal numbers doesn't have to be too difficult, especially with the worksheets below where the decimals work out nicely. To make these worksheets, we randomly generated a divisor and a quotient first, then multiplied them together to get the dividend. Of course, you will see the quotients only on the answer page, but generating questions in this way makes every decimal division problem work out nicely.</p></li>
<li><input type="checkbox" class="list-checkbox" id="multiplying-dividing-decimals-62"><label for="multiplying-dividing-decimals-62" class="wtitle">Decimal Long Division with Quotients That Work Out Nicely</label>
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<a href="decimal/decimals_division_various_various_001.html" class="">Dividing Decimals by Various Decimals with Various Sizes of Quotients</a>
<a href="decimal/decimals_division_tenths_001.html" class="">Dividing Decimals by 1-Digit Tenths (e.g. 0.72 ÷ 0.8 = 0.9)</a>
<a href="decimal/decimals_division_ones_tenths_easy_001.html" class="">Dividing Decimals by 1-Digit Tenths with Larger Quotients (e.g. 3.2 ÷ 0.5 = 6.4)</a>