diff --git a/public/dimensional_analysis.py b/public/dimensional_analysis.py
index bb03db12..a9c5d40e 100644
--- a/public/dimensional_analysis.py
+++ b/public/dimensional_analysis.py
@@ -69,6 +69,8 @@
     Integer
 )
 
+from sympy import S
+
 class ExprWithAssumptions(Expr):
     is_finite: bool
     is_integer: bool
@@ -867,7 +869,22 @@ def custom_latex(expression: Expr) -> str:
 
 _range = Function("_range")
 
-def ensure_dims_all_compatible(*args):
+def dimensional_dependencies_equal(input1, input2):
+    keys1 = set(input1.keys())
+    keys2 = set(input2.keys())
+
+    for key in keys1 ^ keys2: # symmetric difference
+        if input1.get(key, S.Zero).round(EXP_NUM_DIGITS) != S.Zero or \
+           input2.get(key, S.Zero).round(EXP_NUM_DIGITS) != S.Zero:
+            return False
+        
+    for key in keys1 & keys2: # union
+        if input1[key].round(EXP_NUM_DIGITS) != input2[key].round(EXP_NUM_DIGITS):
+            return False
+    
+    return True
+
+def ensure_dims_all_compatible(*args, error_message=None):
     if args[0].is_zero:
         if all(arg.is_zero for arg in args):
             first_arg = sympify('0')
@@ -880,10 +897,14 @@ def ensure_dims_all_compatible(*args):
         return first_arg
 
     first_arg_dims = custom_get_dimensional_dependencies(first_arg)
-    if all(custom_get_dimensional_dependencies(arg) == first_arg_dims for arg in args[1:]):
+
+    if all(dimensional_dependencies_equal(custom_get_dimensional_dependencies(arg), first_arg_dims) for arg in args[1:]):
         return first_arg
 
-    raise TypeError('All input arguments to function need to have compatible units')
+    if error_message is None:
+        raise TypeError('All input arguments to function need to have compatible units')
+    else:
+        raise TypeError(error_message)
 
 def ensure_dims_all_compatible_scalar_or_matrix(*args):
     if len(args) == 1 and is_matrix(args[0]):
@@ -1161,7 +1182,8 @@ def custom_integral_dims(local_expr: Expr, global_expr: Expr, dummy_integral_var
         return global_expr * integral_var # type: ignore
     
 def custom_add_dims(*args: Expr):
-    return Add(*[Abs(arg) for arg in args])
+    return ensure_dims_all_compatible(*[Abs(arg) for arg in args],
+                                      error_message="Only equivalent dimensions can be added or subtracted.")
 
 def custom_pow(base: Expr, exponent: Expr):
     large_rational = False
diff --git a/tests/test_basic.spec.mjs b/tests/test_basic.spec.mjs
index 95ea83d8..192a1110 100644
--- a/tests/test_basic.spec.mjs
+++ b/tests/test_basic.spec.mjs
@@ -780,6 +780,28 @@ test('Test zero canceling bug with exponent', async () => {
   expect(content).toBe('m');
 });
 
+test('Test floating point exponent rounding', async () => {
+
+  await page.setLatex(0, String.raw`1\left\lbrack m\right\rbrack+1\left\lbrack\frac{N^{\frac13}}{m^{\frac23}}\right\rbrack\cdot1\left\lbrack\frac{m^{\frac53}}{N^{\frac13}}\right\rbrack=`);
+  await page.click('#add-math-cell');
+  await page.setLatex(1, String.raw`1\left\lbrack N\cdot s^{.0000000000001}\right\rbrack+2\left\lbrack N\right\rbrack=`);
+  await page.click('#add-math-cell');
+  await page.setLatex(2, String.raw`1\left\lbrack N\cdot s^{.000000000001}\right\rbrack+2\left\lbrack N\right\rbrack=`);
+
+  await page.waitForSelector('text=Updating...', {state: 'detached'});
+
+  let content = await page.textContent('#result-value-0');
+  expect(parseLatexFloat(content)).toBeCloseTo(2, precision);  
+  content = await page.textContent('#result-units-0');
+  expect(content).toBe('m');
+
+  content = await page.textContent('#result-value-1');
+  expect(parseLatexFloat(content)).toBeCloseTo(3, precision);  
+  content = await page.textContent('#result-units-1');
+  expect(content).toBe('N');
+
+  await expect(page.locator('#cell-2 >> text=Dimension Error')).toBeVisible();
+});
 
 test('Test function notation with integrals', async () => {