diff --git a/base/missing.jl b/base/missing.jl
index 744f2e5f149b08..a5c62819b5b004 100644
--- a/base/missing.jl
+++ b/base/missing.jl
@@ -48,7 +48,7 @@ isless(::Missing, ::Any) = false
 isless(::Any, ::Missing) = true
 
 # Unary operators/functions
-for f in (:(!), :(+), :(-), :(identity), :(zero),
+for f in (:(!), :(+), :(-), :(identity), :(zero), :(one), :(oneunit),
           :(abs), :(abs2), :(sign),
           :(acos), :(acosh), :(asin), :(asinh), :(atan), :(atanh),
           :(sin), :(sinh), :(cos), :(cosh), :(tan), :(tanh),
@@ -60,9 +60,12 @@ for f in (:(!), :(+), :(-), :(identity), :(zero),
     @eval Math.$(f)(::Missing) = missing
 end
 
-zero(::Type{Union{T, Missing}}) where {T} = zero(T)
-# To prevent StackOverflowError
-zero(::Type{Any}) = throw(MethodError(zero, (Any,)))
+for f in (:(Base.zero), :(Base.one), :(Base.oneunit))
+    @eval function $(f)(::Type{Union{T, Missing}}) where T
+        T === Any && throw(MethodError($f, (Any,)))  # To prevent StackOverflowError
+        $f(T)
+    end
+end
 
 # Binary operators/functions
 for f in (:(+), :(-), :(*), :(/), :(^),
@@ -112,4 +115,4 @@ function float(A::AbstractArray{Union{T, Missing}}) where {T}
     U = typeof(float(zero(T)))
     convert(AbstractArray{Union{U, Missing}}, A)
 end
-float(A::AbstractArray{Missing}) = A
\ No newline at end of file
+float(A::AbstractArray{Missing}) = A
diff --git a/test/missing.jl b/test/missing.jl
index 6910b1dbcdf86d..54d8e1de9d2552 100644
--- a/test/missing.jl
+++ b/test/missing.jl
@@ -105,13 +105,20 @@ end
     @test ismissing(missing * "a")
 end
 
+# Emulate a unitful type such as Dates.Minute
+struct Unit
+    value::Int
+end
+Base.zero(::Type{Unit}) = Unit(0)
+Base.one(::Type{Unit}) = 1
+
 @testset "elementary functions" begin
     elementary_functions = [abs, abs2, sign,
                             acos, acosh, asin, asinh, atan, atanh, sin, sinh,
                             conj, cos, cosh, tan, tanh,
                             exp, exp2, expm1, log, log10, log1p, log2,
                             exponent, sqrt, gamma, lgamma,
-                            identity, zero,
+                            identity, zero, one, oneunit,
                             iseven, isodd, ispow2,
                             isfinite, isinf, isnan, iszero,
                             isinteger, isreal, isempty, transpose, float]
@@ -121,11 +128,21 @@ end
         @test ismissing(f(missing))
     end
 
-    @test zero(Union{Int, Missing}) === 0
-    @test zero(Union{Float64, Missing}) === 0.0
+    for T in (Int, Float64)
+        @test zero(Union{T, Missing}) === T(0)
+        @test one(Union{T, Missing}) === T(1)
+        @test oneunit(Union{T, Missing}) === T(1)
+    end
+
+    for T in (Unit,)
+        @test zero(Union{T, Missing}) === T(0)
+        @test one(Union{T, Missing}) === 1
+        @test oneunit(Union{T, Missing}) === T(1)
+    end
+
     @test_throws MethodError zero(Any)
-    @test_throws MethodError zero(String)
-    @test_throws MethodError zero(Union{String, Missing})
+    @test_throws MethodError one(Any)
+    @test_throws MethodError oneunit(Any)
 end
 
 @testset "rounding functions" begin