diff --git a/test/basis/test_numerical_accuracy.jl b/test/basis/test_numerical_accuracy.jl
new file mode 100644
index 0000000..ccd991f
--- /dev/null
+++ b/test/basis/test_numerical_accuracy.jl
@@ -0,0 +1,82 @@
+# Test that numerical filtering produces clean fractions
+# Verify the improved round_coefficient function works correctly
+using Test
+using StaticArrays, Tensors
+
+include("../../src/topology/api.jl")
+include("../../src/topology/segments.jl")
+include("../../src/topology/triangles.jl")
+include("../../src/topology/quadrilaterals.jl")
+include("../../src/topology/tetrahedra.jl")
+include("../../src/topology/hexahedra.jl")
+include("../../src/topology/pyramids.jl")
+include("../../src/topology/wedges.jl")
+include("../../src/basis/api.jl")
+include("../../src/basis/basis_generated.jl")
+
+@testset "Numerical Accuracy - Clean Fractions" begin
+    @testset "Hex27 corner nodes - 1/18 coefficients" begin
+        # At origin, all corner nodes should have specific fraction contributions
+        N = get_basis_functions(Hex27(), Lagrange{2}(), Vec{3}((0.0, 0.0, 0.0)))
+
+        # The linear terms in corner shape functions should be exactly 1/18
+        # We can't test the internal expression, but we can verify the partition of unity
+        @test sum(N) ≈ 1.0 atol = 1e-14
+        @test length(N) == 27
+
+        # Center node (N27) should be 1 at center
+        @test N[27] ≈ 1.0 atol = 1e-14
+
+        # All other nodes should be 0 at center
+        @test all(N[1:26] .≈ 0.0)
+    end
+
+    @testset "Hex27 mid-edge nodes - 5/18 coefficients" begin
+        # At a mid-edge location, verify partition of unity
+        N = get_basis_functions(Hex27(), Lagrange{2}(), Vec{3}((0.5, 0.0, 0.0)))
+        @test sum(N) ≈ 1.0 atol = 1e-14
+    end
+
+    @testset "Common fractions in all elements" begin
+        # Test that basis functions evaluate without numerical noise
+
+        # 1/2 (Seg2)
+        N = get_basis_functions(Seg2(), Lagrange{1}(), Vec{1}((0.0,)))
+        @test N[1] ≈ 0.5 atol = 1e-14
+        @test N[2] ≈ 0.5 atol = 1e-14
+
+        # 1/3 (Tri3 at centroid)
+        N = get_basis_functions(Tri3(), Lagrange{1}(), Vec{2}((1 / 3, 1 / 3)))
+        @test N[1] ≈ 1 / 3 atol = 1e-14
+        @test N[2] ≈ 1 / 3 atol = 1e-14
+        @test N[3] ≈ 1 / 3 atol = 1e-14
+
+        # 1/4 (Quad4 at center)
+        N = get_basis_functions(Quad4(), Lagrange{1}(), Vec{2}((0.0, 0.0)))
+        @test all(N .≈ 0.25)
+
+        # 1/8 (Hex8 at center)
+        N = get_basis_functions(Hex8(), Lagrange{1}(), Vec{3}((0.0, 0.0, 0.0)))
+        @test all(N .≈ 0.125)
+    end
+
+    @testset "Higher-order elements - no numerical noise" begin
+        # Quad9 at various points
+        N = get_basis_functions(Quad9(), Lagrange{2}(), Vec{2}((0.3, 0.7)))
+        @test sum(N) ≈ 1.0 atol = 1e-14
+        @test !any(isnan, N)
+        @test !any(isinf, N)
+
+        # Tet10 at various points
+        N = get_basis_functions(Tet10(), Lagrange{2}(), Vec{3}((0.1, 0.2, 0.3)))
+        @test sum(N) ≈ 1.0 atol = 1e-14
+        @test !any(isnan, N)
+        @test !any(isinf, N)
+
+        # Hex20 at various points (uses Serendipity basis)
+        N = get_basis_functions(Hex20(), Serendipity{2}(), Vec{3}((-0.5, 0.5, 0.0)))
+        @test sum(N) ≈ 1.0 atol = 1e-14
+        @test !any(isnan, N)
+        @test !any(isinf, N)
+    end
+end