diff --git a/src/halfinteger.jl b/src/halfinteger.jl
index fb98314..0065c80 100644
--- a/src/halfinteger.jl
+++ b/src/halfinteger.jl
@@ -81,7 +81,7 @@ function Base.convert(::Type{HalfInteger}, r::Real)
 end
 Base.convert(T::Type{<:Integer}, s::HalfInteger) = iseven(s.numerator) ? convert(T, s.numerator>>1) : throw(InexactError(Symbol(T), T, s))
 Base.convert(T::Type{<:Rational}, s::HalfInteger) = convert(T, s.numerator//2)
-Base.convert(T::Type{<:Real}, s::HalfInteger) = convert(T, s.numerator/2)
+Base.convert(T::Type{<:AbstractFloat}, s::HalfInteger) = convert(T, s.numerator) / T(2)
 Base.convert(::Type{HalfInteger}, s::HalfInteger) = s
 
 # Arithmetic
diff --git a/test/halfinteger.jl b/test/halfinteger.jl
index 3d30d65..2198f9c 100644
--- a/test/halfinteger.jl
+++ b/test/halfinteger.jl
@@ -21,15 +21,21 @@ using WignerSymbols: HalfInteger, ishalfinteger, HalfIntegerRange
         @test_throws ArgumentError HalfInteger(-1000, -999)
 
         # convert methods
-        @test convert(HalfInteger, 2) == HalfInteger(2, 1)
-        @test convert(HalfInteger, 1//2) == HalfInteger(1, 2)
-        @test convert(HalfInteger, 1.5) == HalfInteger(3, 2)
+        @test convert(HalfInteger, 2) === HalfInteger(2, 1)
+        @test convert(HalfInteger, 1//2) === HalfInteger(1, 2)
+        @test convert(HalfInteger, 1.5) === HalfInteger(3, 2)
         @test_throws InexactError convert(HalfInteger, 1//3)
         @test_throws InexactError convert(HalfInteger, 0.6)
-        @test convert(HalfInteger, 2) == 2
-        @test convert(HalfInteger, 1//2) == 1//2
-        @test convert(HalfInteger, 1.5) == 1.5
+        @test convert(HalfInteger, 2) === HalfInteger(2, 1)
+        @test convert(HalfInteger, 1//2) === HalfInteger(1, 2)
+        @test convert(HalfInteger, 1.5) === HalfInteger(3, 2)
+
+        @test convert(Integer, HalfInteger(2, 1)) === 2
         @test_throws InexactError convert(Integer, HalfInteger(1, 2))
+        @test convert(Float64, HalfInteger(3, 2)) isa Float64
+        @test convert(Float32, HalfInteger(3, 2)) isa Float32
+        @test convert(Float64, HalfInteger(3, 2)) == 1.5
+        @test convert(Real, HalfInteger(3, 2)) === HalfInteger(3, 2)
 
         # single-argument constructor
         @test HalfInteger(0) == HalfInteger(0, 2)