diff --git a/pint/delegates/formatter/_compound_unit_helpers.py b/pint/delegates/formatter/_compound_unit_helpers.py
index 06a8ac2d3..46934c063 100644
--- a/pint/delegates/formatter/_compound_unit_helpers.py
+++ b/pint/delegates/formatter/_compound_unit_helpers.py
@@ -25,7 +25,7 @@
 )
 
 from ...compat import TypeAlias, babel_parse
-from ...util import UnitsContainer
+from ...util import NonReducingUnitsContainer, UnitsContainer
 
 T = TypeVar("T")
 U = TypeVar("U")
@@ -246,6 +246,7 @@ def prepare_compount_unit(
     locale: Locale | str | None = None,
     as_ratio: bool = True,
     registry: UnitRegistry | None = None,
+    empty_numerator_fmt="1",
 ) -> tuple[Iterable[tuple[str, T]], Iterable[tuple[str, T]]]:
     """Format compound unit into unit container given
     an spec and locale.
@@ -257,6 +258,8 @@ def prepare_compount_unit(
 
     if isinstance(unit, UnitsContainer):
         out = unit.items()
+    elif hasattr(unit, "_units") and isinstance(unit._units, NonReducingUnitsContainer):
+        out = unit._units.non_reduced_d_items
     elif hasattr(unit, "_units"):
         out = unit._units.items()
     else:
diff --git a/pint/delegates/formatter/_format_helpers.py b/pint/delegates/formatter/_format_helpers.py
index 8a2f37a59..429c0ba5f 100644
--- a/pint/delegates/formatter/_format_helpers.py
+++ b/pint/delegates/formatter/_format_helpers.py
@@ -163,6 +163,7 @@ def formatter(
     power_fmt: str = "{} ** {}",
     parentheses_fmt: str = "({0})",
     exp_call: FORMATTER = "{:n}".format,
+    empty_numerator_fmt="1",
 ) -> str:
     """Format a list of (name, exponent) pairs.
 
@@ -185,6 +186,8 @@ def formatter(
         the format used for parenthesis. (Default value = "({0})")
     exp_call : callable
          (Default value = lambda x: f"{x:n}")
+    empty_numerator_fmt : str
+        the format used for an empty numerator. (Default value = "1")
 
     Returns
     -------
@@ -220,7 +223,7 @@ def formatter(
         return join_u(product_fmt, pos_terms + neg_terms)
 
     # Show as Ratio: positive terms / negative terms
-    pos_ret = join_u(product_fmt, pos_terms) or "1"
+    pos_ret = join_u(product_fmt, pos_terms) or empty_numerator_fmt
 
     if not neg_terms:
         return pos_ret
diff --git a/pint/delegates/formatter/full.py b/pint/delegates/formatter/full.py
index d5de43326..5133e0691 100644
--- a/pint/delegates/formatter/full.py
+++ b/pint/delegates/formatter/full.py
@@ -16,7 +16,7 @@
 
 from ..._typing import Magnitude
 from ...compat import Unpack, babel_parse
-from ...util import iterable
+from ...util import NonReducingUnitsContainer, iterable
 from ._compound_unit_helpers import BabelKwds, SortFunc, sort_by_unit_name
 from ._to_register import REGISTERED_FORMATTERS
 from .html import HTMLFormatter
@@ -40,6 +40,11 @@
     from ...registry import UnitRegistry
 
 
+def _sort_func(items, registry):
+    # print([i for i in items])
+    return items
+
+
 class FullFormatter(BaseFormatter):
     """A formatter that dispatch to other formatters.
 
@@ -134,8 +139,16 @@ def format_unit(
     ) -> str:
         uspec = uspec or self.default_format
         sort_func = sort_func or self.default_sort_func
+        empty_numerator_fmt = "1"
+        if isinstance(unit._units, NonReducingUnitsContainer):
+            sort_func = _sort_func
+            empty_numerator_fmt = ""
         return self.get_formatter(uspec).format_unit(
-            unit, uspec, sort_func=sort_func, **babel_kwds
+            unit,
+            uspec,
+            sort_func=sort_func,
+            empty_numerator_fmt=empty_numerator_fmt,
+            **babel_kwds,
         )
 
     def format_quantity(
diff --git a/pint/delegates/formatter/plain.py b/pint/delegates/formatter/plain.py
index d40ec1ae0..5cf77f3e0 100644
--- a/pint/delegates/formatter/plain.py
+++ b/pint/delegates/formatter/plain.py
@@ -81,6 +81,7 @@ def format_unit(
         unit: PlainUnit | Iterable[tuple[str, Any]],
         uspec: str = "",
         sort_func: SortFunc | None = None,
+        empty_numerator_fmt="1",
         **babel_kwds: Unpack[BabelKwds],
     ) -> str:
         """Format a unit (can be compound) into string
@@ -203,6 +204,7 @@ def format_unit(
         unit: PlainUnit | Iterable[tuple[str, Any]],
         uspec: str = "",
         sort_func: SortFunc | None = None,
+        empty_numerator_fmt="1",
         **babel_kwds: Unpack[BabelKwds],
     ) -> str:
         numerator, denominator = prepare_compount_unit(
@@ -225,6 +227,7 @@ def format_unit(
             division_fmt=division_fmt,
             power_fmt="{}**{}",
             parentheses_fmt=r"({})",
+            empty_numerator_fmt=empty_numerator_fmt,
         )
 
     def format_quantity(
@@ -313,6 +316,7 @@ def format_unit(
         unit: PlainUnit | Iterable[tuple[str, Any]],
         uspec: str = "",
         sort_func: SortFunc | None = None,
+        empty_numerator_fmt="1",
         **babel_kwds: Unpack[BabelKwds],
     ) -> str:
         numerator, denominator = prepare_compount_unit(
@@ -339,6 +343,7 @@ def format_unit(
             power_fmt="{}{}",
             parentheses_fmt="({})",
             exp_call=pretty_fmt_exponent,
+            empty_numerator_fmt=empty_numerator_fmt,
         )
 
     def format_quantity(
diff --git a/pint/facets/plain/quantity.py b/pint/facets/plain/quantity.py
index a18919273..33c85ee07 100644
--- a/pint/facets/plain/quantity.py
+++ b/pint/facets/plain/quantity.py
@@ -206,6 +206,8 @@ def __new__(cls, value, units=None):
         if units is None:
             units = inst.UnitsContainer()
         else:
+            if isinstance(units, list):
+                units = inst._REGISTRY.NonReducingUnitContainer(units)
             if isinstance(units, (UnitsContainer, UnitDefinition)):
                 units = units
             elif isinstance(units, str):
diff --git a/pint/facets/plain/registry.py b/pint/facets/plain/registry.py
index 09fd220ee..7f5a499d3 100644
--- a/pint/facets/plain/registry.py
+++ b/pint/facets/plain/registry.py
@@ -63,7 +63,9 @@
 from ...errors import DimensionalityError, RedefinitionError, UndefinedUnitError
 from ...pint_eval import build_eval_tree
 from ...util import (
+    NonReducingUnitsContainer,
     ParserHelper,
+    UnitsContainer,
     _is_dim,
     create_class_with_registry,
     getattr_maybe_raise,
@@ -72,7 +74,6 @@
     string_preprocessor,
     to_units_container,
 )
-from ...util import UnitsContainer as UnitsContainer
 from .definitions import (
     AliasDefinition,
     CommentDefinition,
@@ -217,6 +218,7 @@ def __init__(
         force_ndarray: bool = False,
         force_ndarray_like: bool = False,
         on_redefinition: str = "warn",
+        auto_reduce_units: bool = True,
         auto_reduce_dimensions: bool = False,
         autoconvert_to_preferred: bool = False,
         preprocessors: list[PreprocessorType] | None = None,
@@ -261,6 +263,9 @@ def __init__(
         #: Action to take in case a unit is redefined. 'warn', 'raise', 'ignore'
         self._on_redefinition = on_redefinition
 
+        #: Determines if units should be reduced on appropriate operations.
+        self.auto_reduce_units = auto_reduce_units
+
         #: Determines if dimensionality should be reduced on appropriate operations.
         self.auto_reduce_dimensions = auto_reduce_dimensions
 
@@ -1258,7 +1263,6 @@ def _parse_units_as_container(
 
         if as_delta:
             cache[input_string] = ret
-
         return ret
 
     def _eval_token(
@@ -1402,7 +1406,20 @@ def _define_op(s: str):
     # TODO: Maybe in the future we need to change it to a more meaningful
     # non-colliding name.
     def UnitsContainer(self, *args: Any, **kwargs: Any) -> UnitsContainer:
-        return UnitsContainer(*args, non_int_type=self.non_int_type, **kwargs)
+        return UnitsContainer(
+            *args,
+            non_int_type=self.non_int_type,
+            auto_reduce_units=self.auto_reduce_units,
+            **kwargs,
+        )
+
+    def NonReducingUnitsContainer(self, *args: Any, **kwargs: Any) -> UnitsContainer:
+        return NonReducingUnitsContainer(
+            *args,
+            non_int_type=self.non_int_type,
+            auto_reduce_units=self.auto_reduce_units,
+            **kwargs,
+        )
 
     __call__ = parse_expression
 
diff --git a/pint/registry.py b/pint/registry.py
index ceb9b62d1..c0c0e96ce 100644
--- a/pint/registry.py
+++ b/pint/registry.py
@@ -120,6 +120,7 @@ def __init__(
         autoconvert_offset_to_baseunit: bool = False,
         on_redefinition: str = "warn",
         system=None,
+        auto_reduce_units=True,
         auto_reduce_dimensions=False,
         autoconvert_to_preferred=False,
         preprocessors=None,
@@ -136,6 +137,7 @@ def __init__(
             default_as_delta=default_as_delta,
             autoconvert_offset_to_baseunit=autoconvert_offset_to_baseunit,
             system=system,
+            auto_reduce_units=auto_reduce_units,
             auto_reduce_dimensions=auto_reduce_dimensions,
             autoconvert_to_preferred=autoconvert_to_preferred,
             preprocessors=preprocessors,
diff --git a/pint/testsuite/test_unit.py b/pint/testsuite/test_unit.py
index 2156bbafd..7ce1a84e4 100644
--- a/pint/testsuite/test_unit.py
+++ b/pint/testsuite/test_unit.py
@@ -832,6 +832,36 @@ def test_case_sensitivity(self):
         assert ureg.parse_units("j", case_sensitive=False) == UnitsContainer(joule=1)
 
 
+class TestNonReducing(QuantityTestCase):
+    def test_init(self):
+        ureg = self.ureg
+        NRUC_ = ureg.NonReducingUnitsContainer
+
+        strain_unit_container = NRUC_([(ureg.mm, 1), (ureg.mm, -1)])
+        assert strain_unit_container.non_reduced_units == [
+            ureg.UnitsContainer({"millimeter": 1}),
+            ureg.UnitsContainer({"millimeter": -1}),
+        ]
+        assert strain_unit_container == ureg.dimensionless
+
+    def test_ureg_auto_reduce_units(self):
+        ureg = UnitRegistry(auto_reduce_units=False)
+        NRUC_ = ureg.NonReducingUnitsContainer
+
+        strain_unit = ureg.Unit("mm") / ureg.Unit("mm")
+        strain_unit == NRUC_([(ureg.mm, 1), (ureg.mm, -1)])
+        strain_unit == ureg.Unit("dimensionless")
+
+        strain_q = ureg.Quantity(1, "mm") / ureg.Quantity(1, "mm")
+        assert strain_q.units == strain_unit
+
+    def test_formatting(self):
+        ureg = UnitRegistry(auto_reduce_units=False)
+        strain_unit = ureg.Unit("mm") / ureg.Unit("mm")
+        assert format(strain_unit, "~D") == "mm / mm"
+        assert format(strain_unit, "P") == "millimeter/millimeter"
+
+
 class TestCaseInsensitiveRegistry(QuantityTestCase):
     kwargs = dict(case_sensitive=False)
 
diff --git a/pint/util.py b/pint/util.py
index c7a7ec10c..9e2dc5b07 100644
--- a/pint/util.py
+++ b/pint/util.py
@@ -442,15 +442,20 @@ class UnitsContainer(Mapping[str, Scalar]):
         Numerical type used for non integer values.
     """
 
-    __slots__ = ("_d", "_hash", "_one", "_non_int_type")
+    __slots__ = ("_d", "_hash", "_one", "_non_int_type", "_auto_reduce_units")
 
     _d: udict
     _hash: int | None
     _one: Scalar
     _non_int_type: type
+    _auto_reduce_units: bool
 
     def __init__(
-        self, *args: Any, non_int_type: type | None = None, **kwargs: Any
+        self,
+        *args: Any,
+        non_int_type: type | None = None,
+        auto_reduce_units: bool = True,
+        **kwargs: Any,
     ) -> None:
         if args and isinstance(args[0], UnitsContainer):
             default_non_int_type = args[0]._non_int_type
@@ -458,6 +463,7 @@ def __init__(
             default_non_int_type = float
 
         self._non_int_type = non_int_type or default_non_int_type
+        self._auto_reduce_units = auto_reduce_units
 
         if self._non_int_type is float:
             self._one = 1
@@ -620,13 +626,20 @@ def __copy__(self):
         out._hash = self._hash
         out._non_int_type = self._non_int_type
         out._one = self._one
+        out._auto_reduce_units = self._auto_reduce_units
         return out
 
+    def __deepcopy__(self, memo):
+        return self.copy()
+
     def __mul__(self, other: Any):
-        if not isinstance(other, self.__class__):
+        if not isinstance(other, UnitsContainer):
             err = "Cannot multiply UnitsContainer by {}"
             raise TypeError(err.format(type(other)))
 
+        if not self._auto_reduce_units:
+            return NonReducingUnitsContainer([self, other])
+
         new = self.copy()
         for key, value in other.items():
             new._d[key] += value
@@ -650,10 +663,13 @@ def __pow__(self, other: Any):
         return new
 
     def __truediv__(self, other: Any):
-        if not isinstance(other, self.__class__):
+        if not isinstance(other, UnitsContainer):
             err = "Cannot divide UnitsContainer by {}"
             raise TypeError(err.format(type(other)))
 
+        if not self._auto_reduce_units:
+            return NonReducingUnitsContainer([self, UnitsContainer({}) / other])
+
         new = self.copy()
         for key, value in other.items():
             new._d[key] -= self._normalize_nonfloat_value(value)
@@ -664,7 +680,7 @@ def __truediv__(self, other: Any):
         return new
 
     def __rtruediv__(self, other: Any):
-        if not isinstance(other, self.__class__) and other != 1:
+        if not isinstance(other, UnitsContainer) and other != 1:
             err = "Cannot divide {} by UnitsContainer"
             raise TypeError(err.format(type(other)))
 
@@ -676,6 +692,52 @@ def _normalize_nonfloat_value(self, value: Scalar) -> Scalar:
         return value
 
 
+class NonReducingUnitsContainer(UnitsContainer):
+    """The NonReducingUnitsContainer stores UnitsContainers without simplifying common units.
+    This is useful when it is desired to show a unit in the numerator and denominator, eg mm/mm.
+    """
+
+    def __init__(
+        self,
+        units: list[UnitsContainer] | list[tuple[QuantityOrUnitLike, Scalar]],
+        non_int_type: type | None = None,
+        auto_reduce_units: bool = True,
+    ) -> None:
+        self.non_reduced_units = []
+        self._non_int_type = non_int_type
+        self.auto_reduce_units = auto_reduce_units
+
+        for u in units:
+            if isinstance(u, tuple):
+                u = u[0]._units ** u[1]
+            if hasattr(u, "_units"):
+                u = u._units
+            self.non_reduced_units.append(u)
+
+        self.reduced_units = UnitsContainer()
+        for unit in self.non_reduced_units:
+            self.reduced_units *= unit
+
+        self._d = self.reduced_units._d
+        self._hash = self.reduced_units._hash
+
+        self.non_reduced_d_items = [
+            (key, value)
+            for uc in self.non_reduced_units
+            for key, value in uc._d.items()
+        ]
+        self.i = 0
+
+    def __repr__(self) -> str:
+        tmp = "[%s]" % ", ".join(
+            [f"'{key}': {value}" for key, value in self.non_reduced_d_items]
+        )
+        return f"<NonReducingUnitsContainer({tmp})>"
+
+    def unit_items(self) -> Iterable[tuple[str, Scalar]]:
+        return [items for _d in self.non_reduced_units for items in _d.items()]
+
+
 class ParserHelper(UnitsContainer):
     """The ParserHelper stores in place the product of variables and
     their respective exponent and implements the corresponding operations.