diff --git a/src/FixedPointNumbers.jl b/src/FixedPointNumbers.jl
index fd0abb95..a5b0848d 100644
--- a/src/FixedPointNumbers.jl
+++ b/src/FixedPointNumbers.jl
@@ -4,7 +4,7 @@ import Base: ==, <, <=, -, +, *, /, ~, isapprox,
              convert, promote_rule, show, isinteger, abs, decompose,
              isnan, isinf, isfinite,
              zero, oneunit, one, typemin, typemax, floatmin, floatmax, eps, reinterpret,
-             float, trunc, round, floor, ceil, bswap,
+             big, rationalize, float, trunc, round, floor, ceil, bswap,
              div, fld, rem, mod, mod1, fld1, min, max, minmax,
              rand, length
 
@@ -71,6 +71,14 @@ function (::Type{Ti})(x::FixedPoint) where {Ti <: Integer}
 end
 Base.Rational{Ti}(x::FixedPoint) where {Ti <: Integer} = Rational{Ti}(Rational(x))
 
+big(::Type{<:FixedPoint}) = BigFloat
+big(x::FixedPoint) = convert(BigFloat, x)
+
+rationalize(x::FixedPoint; tol::Real=eps(x)) = rationalize(Int, x, tol=tol)
+function rationalize(::Type{Ti}, x::FixedPoint; tol::Real=eps(x)) where Ti <: Integer
+    tol <= eps(x) ? Rational{Ti}(x) : rationalize(Ti, float(x), tol)
+end
+
 """
     isapprox(x::FixedPoint, y::FixedPoint; rtol=0, atol=max(eps(x), eps(y)))
 
diff --git a/src/normed.jl b/src/normed.jl
index 0593567a..b34ae065 100644
--- a/src/normed.jl
+++ b/src/normed.jl
@@ -244,7 +244,7 @@ function Base.Float64(x::Normed{UInt128,f}) where f
     end
 end
 
-Base.BigFloat(x::Normed) = reinterpret(x)*(1/BigFloat(rawone(x)))
+Base.BigFloat(x::Normed) = reinterpret(x) / BigFloat(rawone(x))
 
 Base.Rational(x::Normed) = reinterpret(x)//rawone(x)
 
diff --git a/test/fixed.jl b/test/fixed.jl
index 2657ff08..7285b061 100644
--- a/test/fixed.jl
+++ b/test/fixed.jl
@@ -253,14 +253,6 @@ end
     @test varm(a, m) === varm(af, m)
 end
 
-@testset "convert result type" begin
-    x = Fixed{Int8,7}(0.75)
-    for T in (Float16, Float32, Float64, BigFloat)
-        y = convert(T, x)
-        @test isa(y, T)
-    end
-end
-
 @testset "bool conversions" begin
     @test convert(Bool, 0.0Q1f6) === false
     @test convert(Bool, 1.0Q1f6) === true
@@ -269,7 +261,7 @@ end
     @test_broken convert(Bool, Fixed{Int8,8}(0.2)) # TODO: remove this
 end
 
-@testset "Integer conversions" begin
+@testset "integer conversions" begin
     @test convert(Int, Q1f6(1)) === 1
     @test convert(Integer, Q1f6(1)) === Int8(1)
     @test convert(UInt, 1Q1f6) === UInt(1)
@@ -280,7 +272,19 @@ end
 @testset "rational conversions" begin
     @test convert(Rational, -0.75Q1f6) === Rational{Int8}(-3//4)
     @test convert(Rational, -0.75Q0f7) === Rational{Int16}(-3//4)
-    @test convert(Rational{Int}, -0.75Q0f7) === Rational(-3//4)
+    @test convert(Rational{Int}, -0.75Q0f7) === Rational{Int}(-3//4)
+
+    @test rationalize(-0.75Q3f4) === Rational{Int}(-3//4)
+    @test rationalize(Int16, 0.81Q3f4) === Rational{Int16}(13//16)
+    @test rationalize(-0.81Q3f4, tol=0.02) === Rational{Int}(-13//16)
+    @test rationalize(Int8, -0.81Q3f4, tol=0.07) === Rational{Int8}(-3//4)
+end
+
+@testset "BigFloat conversions" begin
+    @test convert(BigFloat, -0.75Q0f7)::BigFloat == big"-0.75"
+
+    @test big(Q7f0) === BigFloat # !== BigInt
+    @test big(0.75Q3f4)::BigFloat == big"0.75"
 end
 
 @testset "Floating-point conversions" begin
@@ -290,7 +294,7 @@ end
 end
 
 @testset "conversions to float" begin
-    for T in (Float16, Float32, Float64, BigFloat)
+    for T in (Float16, Float32, Float64)
         @test isa(convert(T, Q0f7(0.3)), T)
     end
 
diff --git a/test/normed.jl b/test/normed.jl
index 44b8f33e..dd101b8e 100644
--- a/test/normed.jl
+++ b/test/normed.jl
@@ -110,7 +110,6 @@ end
         @test convert(Integer, one(T)) == 1
         @test convert(Rational, one(T)) == 1
     end
-    @test convert(Rational, convert(N0f8, 0.5)) == 0x80//0xff
     @test convert(N0f16, one(N0f8)) === one(N0f16)
     @test convert(N0f16, N0f8(0.5)).i === 0x8080
     @test convert(Normed{UInt16,7}, Normed{UInt8,7}(0.504)) === Normed{UInt16,7}(0.504)
@@ -124,6 +123,24 @@ end
     @test_throws InexactError convert(Int8, 256N8f8)
 end
 
+@testset "rational conversions" begin
+    @test convert(Rational, 0.5N0f8) === Rational{UInt8}(0x80//0xff)
+    @test convert(Rational, 0.5N4f12) === Rational{UInt16}(0x800//0xfff)
+    @test convert(Rational{Int}, 0.5N0f8) === Rational{Int}(0x80//0xff)
+
+    @test rationalize(0.8N0f8) === Rational{Int}(4//5)
+    @test rationalize(Int16, 0.804N0f8) === Rational{Int16}(41//51)
+    @test rationalize(0.804N0f8, tol=0.002) === Rational{Int}(41//51)
+    @test rationalize(Int8, 0.804N0f8, tol=0.005) === Rational{Int8}(4//5)
+end
+
+@testset "BigFloat conversions" begin
+    @test convert(BigFloat, 0.5N0f8)::BigFloat == 128 / big"255"
+
+    @test big(N7f1) === BigFloat # !== BigInt
+    @test big(0.5N4f4)::BigFloat == 8 / big"15"
+end
+
 @testset "conversion from float" begin
     # issue 102
     for T in (UInt8, UInt16, UInt32, UInt64, UInt128)
@@ -158,7 +175,7 @@ end
 
 @testset "conversions to float" begin
     x = N0f8(0.3)
-    for T in (Float16, Float32, Float64, BigFloat)
+    for T in (Float16, Float32, Float64)
         y = convert(T, x)
         @test isa(y, T)
     end