diff --git a/src/conversion.jl b/src/conversion.jl
index 8a32ac63..e244911a 100644
--- a/src/conversion.jl
+++ b/src/conversion.jl
@@ -1,3 +1,24 @@
+"""
+    UnitConversionFactor(x::AbstractFloat)
+Conversion factor with value `x`.
+
+Used by the [`convfact`](@ref) function to preserve
+the floating-point precision of quantities.
+"""
+struct UnitConversionFactor{T<:AbstractFloat} <: AbstractIrrational
+    x::T
+    # the inner constructor necessary for ambiguity resolution
+    UnitConversionFactor(x::T) where {T<:AbstractFloat} = new{T}(x) 
+end
+
+Base.:*(a::UnitConversionFactor, b::BigFloat) = a.x * b
+Base.:*(a::BigFloat, b::UnitConversionFactor) = a * b.x
+Base.:(==)(a::UnitConversionFactor, b::UnitConversionFactor) = a.x == b.x
+Base.hash(x::UnitConversionFactor, h::UInt) = hash(x.x, h)
+Base.BigFloat(x::UnitConversionFactor) = BigFloat(x.x)
+Base.Float64(x::UnitConversionFactor) = Float64(x.x)
+Base.Float32(x::UnitConversionFactor) = Float32(x.x)
+
 """
     convfact(s::Units, t::Units)
 Find the conversion factor from unit `t` to unit `s`, e.g., `convfact(m, cm) == 1//100`.
@@ -37,7 +58,7 @@ Find the conversion factor from unit `t` to unit `s`, e.g., `convfact(m, cm) ==
             "exponents and/or SI prefixes in units"
         ))
     end
-    return :($result)
+    return result isa AbstractFloat ? UnitConversionFactor(result) : result
 end
 
 """
diff --git a/test/runtests.jl b/test/runtests.jl
index cfc39070..dd32a39d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -228,6 +228,24 @@ end
             # Issue 647:
             @test uconvert(u"kb^1000", 1u"kb^1001 * b^-1") === 1000u"kb^1000"
             @test uconvert(u"kOe^1000", 1u"kOe^1001 * Oe^-1") === 1000u"kOe^1000"
+            # Issue 753:
+            # preserve the floating-point precision of quantities
+            @test Unitful.numtype(uconvert(m, BigFloat(100)cm)) === BigFloat
+            @test Unitful.numtype(uconvert(cm, (BigFloat(1)π + im) * m)) === Complex{BigFloat}
+            @test Unitful.numtype(uconvert(rad, BigFloat(360)°)) === BigFloat
+            @test Unitful.numtype(uconvert(°, (BigFloat(2)π + im) * rad)) === Complex{BigFloat}
+            @test Unitful.numtype(uconvert(m, 100.0cm)) === Float64
+            @test Unitful.numtype(uconvert(cm, (1.0π + im) * m)) === ComplexF64
+            @test Unitful.numtype(uconvert(rad, 360.0°)) === Float64
+            @test Unitful.numtype(uconvert(°, (2.0π + im) * rad)) === ComplexF64
+            @test Unitful.numtype(uconvert(m, 100f0cm)) === Float32
+            @test Unitful.numtype(uconvert(cm, (1f0π + im) * m)) === ComplexF32
+            @test Unitful.numtype(uconvert(rad, 360f0°)) === Float32
+            @test Unitful.numtype(uconvert(°, (2f0π + im) * rad)) === ComplexF32
+            @test Unitful.numtype(uconvert(m, Float16(100)cm)) === Float16
+            @test Unitful.numtype(uconvert(cm, (Float16(1)π + im) * m)) === ComplexF16
+            @test Unitful.numtype(uconvert(rad, Float16(360)°)) === Float16
+            @test Unitful.numtype(uconvert(°, (Float16(2)π + im) * rad)) === ComplexF16
             # Floating point overflow/underflow in uconvert can happen if the
             # conversion factor is large, because uconvert does not cancel
             # common basefactors (or just for really large exponents and/or