diff --git a/brainunit/__init__.py b/brainunit/__init__.py
index c78f24b..fce3ee9 100644
--- a/brainunit/__init__.py
+++ b/brainunit/__init__.py
@@ -15,8 +15,16 @@
 
 __version__ = "0.0.1.1"
 
+import importlib
+
 from . import math
+from . import _base
+from . import _unit_common
+from . import _unit_constants
+from . import _unit_shortcuts
+
 from ._base import *
+from ._base import _default_magnitude, _siprefixes
 from ._base import __all__ as _base_all
 from ._unit_common import *
 from ._unit_common import __all__ as _common_all
@@ -27,3 +35,71 @@
 
 __all__ = ['math'] + _common_all + _std_units_all + _constants_all + _base_all
 del _common_all, _std_units_all, _constants_all, _base_all
+
+
+def set_default_magnitude(
+    magnitude: int | dict[str, int],
+    # unit: Unit = None,
+):
+  """
+  Set the default magnitude for units.
+
+  Parameters
+  ----------
+  magnitude : int | dict[str, int]
+      The magnitude to set. If an int is given, it will be set for all
+      dimensions. If a dict is given, it will be set for the specified
+      dimensions.
+
+  Examples
+  --------
+  >>> set_default_magnitude('n') # Sets the default magnitude to 'nano' (10e-9)
+  >>> set_default_magnitude(-9) # Alternatively, use an integer to represent the exponent of 10
+  >>> set_default_magnitude({'m': -3, 'kg': -9}) # Set the default magnitude for 'metre' to 'milli' and 'kilogram' to 'nano'
+  >>> set_default_magnitude({'m': 'm', 'kg': 'n'}) # Alternatively, use a string to represent the magnitude
+  >>> set_default_magnitude(-3, unit=volt) # Set the default magnitude for the 'volt' unit to 'milli'
+  """
+  global _default_magnitude
+  if isinstance(magnitude, int):
+    # if isinstance(unit, Unit):
+    #   for key, dim in zip(_default_magnitude.keys(), unit.dim._dims):
+    #     _default_magnitude[key] = magnitude / abs(dim) if dim != 0 else 0
+    # else:
+    _default_magnitude.update((key, magnitude) for key in _default_magnitude)
+  elif isinstance(magnitude, str):
+    # if isinstance(unit, Unit):
+    #   for key, dim in zip(_default_magnitude.keys(), unit.dim._dims):
+    #     _default_magnitude[key] = _siprefixes[magnitude] / abs(dim) if dim != 0 else 0
+    # else:
+    _default_magnitude.update((key, _siprefixes[magnitude]) for key in _default_magnitude)
+  elif isinstance(magnitude, dict):
+    _default_magnitude.update((key, 0) for key in _default_magnitude)
+    for key, value in magnitude.items():
+      if isinstance(value, int):
+        _default_magnitude[key] = value
+      elif isinstance(value, str):
+        _default_magnitude[key] = _siprefixes[value]
+      else:
+        raise ValueError(f"Invalid magnitude value: {value}")
+  else:
+    raise ValueError(f"Invalid magnitude: {magnitude}")
+
+  global _unit_common
+  global _unit_constants
+  global _unit_shortcuts
+  # Reload modules
+  importlib.reload(_unit_common)
+  importlib.reload(_unit_constants)
+  importlib.reload(_unit_shortcuts)
+
+  from ._base import __all__ as _base_all
+  from ._unit_common import __all__ as _common_all
+  from ._unit_constants import __all__ as _constants_all
+  from ._unit_shortcuts import __all__ as _std_units_all
+  globals().update({k: getattr(_unit_common, k) for k in _common_all})
+  globals().update({k: getattr(_unit_constants, k) for k in _constants_all})
+  globals().update({k: getattr(_unit_shortcuts, k) for k in _std_units_all})
+
+  global __all__
+  __all__ = ['math'] + _common_all + _std_units_all + _constants_all + _base_all
+  del _common_all, _std_units_all, _constants_all, _base_all
\ No newline at end of file
diff --git a/brainunit/_base.py b/brainunit/_base.py
index 070c439..93d859e 100644
--- a/brainunit/_base.py
+++ b/brainunit/_base.py
@@ -48,7 +48,7 @@
   'check_units',
   'is_scalar_type',
   'fail_for_dimension_mismatch',
-  'assert_quantity'
+  'assert_quantity',
 ]
 
 _all_slice = slice(None, None, None)
@@ -56,6 +56,17 @@
 _allow_python_scalar_value = False
 _auto_register_unit = True
 
+# for setting the default magnitude of the unit
+_default_magnitude = {
+  "m": 0,
+  "kg": 0,
+  "s": 0,
+  "A": 0,
+  "K": 0,
+  "mol": 0,
+  "cd": 0,
+}
+
 
 @contextmanager
 def turn_off_auto_unit_register():
@@ -584,6 +595,31 @@ def get_dim(obj) -> Dimension:
       raise TypeError(f"Object of type {type(obj)} does not have dimensions")
 
 
+def get_unit(obj) -> Unit:
+  """
+  Return the unit of any object that has them.
+
+  Parameters
+  ----------
+  obj : `object`
+      The object to check.
+
+  Returns
+  -------
+  unit : Unit
+      The physical unit of the `obj`.
+  """
+  try:
+    return obj.unit
+  except AttributeError:
+    if isinstance(obj, (numbers.Number, jax.Array, np.number, np.ndarray)):
+      return Unit(1, name='1', dispname='1')
+    try:
+      return Quantity(obj).unit
+    except TypeError:
+      raise TypeError(f"Object of type {type(obj)} does not have a unit")
+
+
 def have_same_unit(obj1, obj2) -> bool:
   """Test if two values have the same dimensions.
 
@@ -969,12 +1005,15 @@ def check_units_and_collect_values(lst):
 
 def _get_dim(dim: Dimension, unit: 'Unit'):
   if dim != DIMENSIONLESS and unit is not None:
-    raise ValueError("Cannot specify both a dimension and a unit")
+    return None, dim
   if dim == DIMENSIONLESS:
     if unit is None:
       return None, DIMENSIONLESS
     else:
-      return unit.value, unit.dim
+      try:
+        return unit.value, unit.dim
+      except:
+        return None, unit.dim
   else:
     return None, dim
 
@@ -987,7 +1026,7 @@ class Quantity(object):
 
   """
   __module__ = "brainunit"
-  __slots__ = ('_value', '_dim')
+  __slots__ = ('_value', '_dim', '_unit')
   _value: Union[jax.Array, numbers.Number]
   _dim: Dimension
   __array_priority__ = 1000
@@ -1005,6 +1044,8 @@ def __init__(
     if isinstance(value, numbers.Number):
       self._dim = dim
       self._value = (value if scale is None else (value * scale))
+      if dim is not DIMENSIONLESS:
+        self._unit = unit
       return
 
     if isinstance(value, (list, tuple)):
@@ -1023,6 +1064,7 @@ def __init__(
     # array value
     if isinstance(value, Quantity):
       self._dim = value.dim
+      self._unit = Unit(1, name='1', dispname='1') if unit is None else unit
       self._value = jnp.array(value.value, dtype=dtype)
       return
 
@@ -1044,6 +1086,12 @@ def __init__(
     # dimension
     self._dim = dim
 
+    # unit
+    if unit is None:
+      self._unit = Unit(1, name='1', dispname='1')
+    else:
+      self._unit = unit
+
   @property
   def value(self) -> jax.Array | numbers.Number:
     # return the value
@@ -1101,7 +1149,8 @@ def dim(self, *args):
 
   @property
   def unit(self) -> 'Unit':
-    return Unit(1., self.dim, register=False)
+    return self._unit
+    # return Unit(1., self.dim, register=False)
 
   @unit.setter
   def unit(self, *args):
@@ -1214,14 +1263,14 @@ def get_best_unit(self, *regs) -> 'Quantity':
         The best unit for this `Array`.
     """
     if self.is_unitless:
-      return Unit(1)
+      return Unit(1, name='1', dispname='1')
     if len(regs):
       for r in regs:
         try:
           return r[self]
         except KeyError:
           pass
-      return Quantity(1, dim=self.dim)
+      return self.unit
     else:
       return self.get_best_unit(standard_unit_register, user_unit_register, additional_unit_register)
 
@@ -1556,6 +1605,7 @@ def _binary_operation(
     """
     other = _to_quantity(other)
     other_dim = None
+    other_unit = None
 
     if fail_for_mismatch:
       if inplace:
@@ -1568,9 +1618,13 @@ def _binary_operation(
     if other_dim is None:
       other_dim = get_dim(other)
 
+    if other_unit is None:
+      other_unit = get_unit(other)
+
     new_dim = unit_operation(self.dim, other_dim)
+    new_unit = unit_operation(self.unit, other_unit)
     result = value_operation(self.value, other.value)
-    r = Quantity(result, dim=new_dim)
+    r = Quantity(result, dim=new_dim, unit=new_unit)
     if inplace:
       self.update_value(r.value)
       return self
@@ -2688,11 +2742,18 @@ def __init__(
     # Whether this unit is a combination of other units
     self.iscompound = iscompound
 
-    super().__init__(value, dtype=dtype, dim=dim)
+    if dim == DIMENSIONLESS:
+      super().__init__(value, dtype=dtype, dim=dim)
+    else:
+      super().__init__(value, dtype=dtype, dim=dim, unit=self)
 
     if _auto_register_unit and register:
       register_new_unit(self)
 
+  @property
+  def unit(self) -> 'Unit':
+    return self
+
   @staticmethod
   def create(unit: Dimension, name: str, dispname: str, scale: int = 0):
     """
@@ -2718,6 +2779,8 @@ def create(unit: Dimension, name: str, dispname: str, scale: int = 0):
     name = str(name)
     dispname = str(dispname)
 
+    scale = calculate_scale(unit=unit, scale=scale)
+
     u = Unit(
       10.0 ** scale,
       dim=unit,
@@ -3274,3 +3337,37 @@ def new_f(*args, **kwds):
     return new_f
 
   return do_check_units
+
+
+def calculate_scale(
+    unit: Dimension,
+    scale: int = 0
+) -> int:
+  """
+  Calculate the scale for a unit.
+
+  Parameters
+  ----------
+  unit : Dimension
+      The unit to determine the scale for.
+
+  Returns
+  -------
+  scale : int
+      The scale for the unit.
+
+  Examples
+  --------
+  >>> set_default_magnitude({'m': -3, 'kg': -9})
+  >>> calculate_scale(get_or_create_dimension(m=1))
+  -3
+  >>> calculate_scale(get_or_create_dimension(kg=1))
+  -9
+  >>> calculate_scale(get_or_create_dimension(m=1, kg=1))
+  -12
+  >>> calculate_scale(get_or_create_dimension(m=2, kg=-1))
+  3
+  """
+  for dim, magnitude in zip(unit._dims, _default_magnitude.values()):
+    scale -= dim * magnitude
+  return scale
diff --git a/brainunit/_unit_test.py b/brainunit/_unit_test.py
index c7401a4..152b9f2 100644
--- a/brainunit/_unit_test.py
+++ b/brainunit/_unit_test.py
@@ -608,7 +608,6 @@ def test_addition_subtraction():
     with pytest.raises(DimensionMismatchError):
       np.array([5], dtype=np.float64) - q
 
-
     # Check that operations with 0 work
     with pytest.raises(DimensionMismatchError):
       assert_quantity(q + 0, q.value, volt)
@@ -1473,3 +1472,123 @@ def f(b):
     return b
 
   f(a)
+
+
+def test_set_default_magnitude_1():
+  bu.set_default_magnitude(-3)
+  # from brainunit import second, ms
+  q1 = 3 * bu.second
+  q2 = 3 * bu.ms
+
+  assert q1.to_value() == 3e3
+  assert q2.to_value() == 3.
+
+  bu.set_default_magnitude(0)
+  # from brainunit import second, ms
+  q1 = 3 * bu.second
+  q2 = 3 * bu.ms
+  assert q1.to_value() == 3.
+  assert q2.to_value() == 3e-3
+
+  bu.set_default_magnitude(3)
+  # from brainunit import second, ms
+  q1 = 3 * bu.second
+  q2 = 3 * bu.ms
+  assert q1.to_value() == 3e-3
+  assert q2.to_value() == 3e-6
+
+def test_set_default_magnitude_2():
+  bu.set_default_magnitude(-3)
+  # from brainunit import second, ms, meter, kmeter
+  q1 = 3 * bu.second * bu.meter
+  q2 = 3 * bu.ms * bu.kmeter
+
+  value = str(q1)
+
+  assert q1.to_value() == 3e6
+  assert q2.to_value() == 3e6
+
+  bu.set_default_magnitude(0)
+  # from brainunit import second, ms, meter, kmeter
+  q1 = 3 * bu.second * bu.meter
+  q2 = 3 * bu.ms * bu.kmeter
+  assert q1.to_value() == 3.
+  assert q2.to_value() == 3.
+
+  bu.set_default_magnitude(3)
+  # from brainunit import second, ms, meter, kmeter
+  q1 = 3 * bu.second * bu.meter
+  q2 = 3 * bu.ms * bu.kmeter
+  assert q1.to_value() == 3e-6
+  assert q2.to_value() == 3e-6
+
+def test_set_default_magnitude_3():
+  bu.set_default_magnitude({'s': 'm'})
+  from brainunit import second, ms, meter, kmeter
+  q1 = 3 * bu.second * bu.meter
+  q2 = 3 * bu.ms * bu.kmeter
+
+  assert q1.to_value() == 3e3
+  assert q2.to_value() == 3e3
+
+  bu.set_default_magnitude(0)
+  # from brainunit import second, ms, meter, kmeter
+  q1 = 3 * bu.second * bu.meter
+  q2 = 3 * bu.ms * bu.kmeter
+  assert q1.to_value() == 3.
+  assert q2.to_value() == 3.
+
+  bu.set_default_magnitude({'s': 3})
+  # from brainunit import second, ms, meter, kmeter
+  q1 = 3 * bu.second * bu.meter
+  q2 = 3 * bu.ms * bu.kmeter
+  assert q1.to_value() == 3e-3
+  assert q2.to_value() == 3e-3
+
+def test_set_default_magnitude_4():
+  # volt: m=2, kg=1, s=-3, A=-1
+  bu.set_default_magnitude(-3)
+  # from brainunit import volt, mV
+  q1 = 3 * bu.volt
+  q2 = 3 * bu.mV
+
+  assert q1.to_value() == 3e-3
+  assert q2.to_value() == 3e-6
+
+  bu.set_default_magnitude(0)
+  # from brainunit import volt, mV
+  q1 = 3 * bu.volt
+  q2 = 3 * bu.mV
+  assert q1.to_value() == 3.
+  assert q2.to_value() == 3e-3
+
+  bu.set_default_magnitude(3)
+  # from brainunit import volt, mV
+  q1 = 3 * bu.volt
+  q2 = 3 * bu.mV
+  assert q1.to_value() == 3e3
+  assert q2.to_value() == 3
+
+# def test_set_default_magnitude_5():
+#   # volt: m=2, kg=1, s=-3, A=-1 --> (if set to milivolt) _default_magnitude = {'m': -1.5, 'kg': -3, 's': -1, 'A': -3} (WRONG!)
+#   bu.set_default_magnitude(-3, unit=bu.volt)
+#   from brainunit import volt, mV
+#   q1 = 3 * volt
+#   q2 = 3 * mV
+#
+#   assert q1.to_value() == 3e3
+#   assert q2.to_value() == 3
+#
+#   bu.set_default_magnitude(0)
+#   from brainunit import volt, mV
+#   q1 = 3 * volt
+#   q2 = 3 * mV
+#   assert q1.to_value() == 3.
+#   assert q2.to_value() == 3e-3
+#
+#   bu.set_default_magnitude(3)
+#   from brainunit import volt, mV
+#   q1 = 3 * volt
+#   q2 = 3 * mV
+#   assert q1.to_value() == 3e-3
+#   assert q2.to_value() == 3e-6
\ No newline at end of file