diff --git a/Project.toml b/Project.toml
index bbdecb05b..be7d74ad5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesCore"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "0.9.19"
+version = "0.9.20"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/differentials/abstract_zero.jl b/src/differentials/abstract_zero.jl
index 5790323ad..4381676d5 100644
--- a/src/differentials/abstract_zero.jl
+++ b/src/differentials/abstract_zero.jl
@@ -24,6 +24,8 @@ Base.adjoint(z::AbstractZero) = z
 Base.transpose(z::AbstractZero) = z
 Base.:/(z::AbstractZero, ::Any) = z
 
+Base.convert(::Type{T}, x::AbstractZero) where T <: Number = zero(T)
+
 """
     Zero() <: AbstractZero
 
diff --git a/test/differentials/abstract_zero.jl b/test/differentials/abstract_zero.jl
index 13cc2b49e..640d1ce6b 100644
--- a/test/differentials/abstract_zero.jl
+++ b/test/differentials/abstract_zero.jl
@@ -59,6 +59,9 @@
         @test complex(z, z) === z
         @test complex(z, 2.0) === Complex{Float64}(0.0, 2.0)
         @test complex(1.5, z) === Complex{Float64}(1.5, 0.0)
+
+        @test convert(Int64, Zero()) == 0
+        @test convert(Float64, Zero()) == 0.0
     end
 
     @testset "DoesNotExist" begin
@@ -96,5 +99,8 @@
             @test f(dne) === dne
         end
         @test dne / 2 === dne / [1, 3] === dne
+
+        @test convert(Int64, DoesNotExist()) == 0
+        @test convert(Float64, DoesNotExist()) == 0.0
     end
 end