diff --git a/base/floatfuncs.jl b/base/floatfuncs.jl
index 2bca2989bab0b..1b3a088524c8e 100644
--- a/base/floatfuncs.jl
+++ b/base/floatfuncs.jl
@@ -225,9 +225,11 @@ end
 """
     isapprox(x, y; atol::Real=0, rtol::Real=atol>0 ? 0 : √eps, nans::Bool=false[, norm::Function])
 
-Inexact equality comparison: `true` if `norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))`. The
-default `atol` is zero and the default `rtol` depends on the types of `x` and `y`. The keyword
-argument `nans` determines whether or not NaN values are considered equal (defaults to false).
+Inexact equality comparison. Two numbers compare equal if their relative distance *or* their
+absolute distance is within tolerance bounds: `isapprox` returns `true` if
+`norm(x-y) <= max(atol, rtol*max(norm(x), norm(y)))`. The default `atol` is zero and the
+default `rtol` depends on the types of `x` and `y`. The keyword argument `nans` determines
+whether or not NaN values are considered equal (defaults to false).
 
 For real or complex floating-point values, if an `atol > 0` is not specified, `rtol` defaults to
 the square root of [`eps`](@ref) of the type of `x` or `y`, whichever is bigger (least precise).
@@ -259,13 +261,16 @@ but an absurdly large tolerance if `x` is the
 
 # Examples
 ```jldoctest
-julia> 0.1 ≈ (0.1 - 1e-10)
+julia> isapprox(0.1, 0.15; atol=0.05)
 true
 
-julia> isapprox(10, 11; atol = 2)
+julia> isapprox(0.1, 0.15; rtol=0.34)
 true
 
-julia> isapprox([10.0^9, 1.0], [10.0^9, 2.0])
+julia> isapprox(0.1, 0.15; rtol=0.33)
+false
+
+julia> 0.1 + 1e-10 ≈ 0.1
 true
 
 julia> 1e-10 ≈ 0
@@ -273,6 +278,9 @@ false
 
 julia> isapprox(1e-10, 0, atol=1e-8)
 true
+
+julia> isapprox([10.0^9, 1.0], [10.0^9, 2.0]) # using `norm`
+true
 ```
 """
 function isapprox(x::Number, y::Number;