# How to test if one float is an integer multiple of another?

**URL:** <https://discourse.julialang.org/t/how-to-test-if-one-float-is-an-integer-multiple-of-another/70745>\
**Category:** General Usage\
**Tags:** question, float\
**Created:** [November 1, 2021, 4:00pm UTC](https://discourse.julialang.org/t/how-to-test-if-one-float-is-an-integer-multiple-of-another/70745 "2021-11-01T16:00:24Z")\
**Posts on this page:** 1\
**Showing post:** 3

<div class="post-metadata">

**Author:** ![rdeits](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rdeits/32/286_2.png) [@rdeits](https://discourse.julialang.org/u/rdeits)\
**Post date:** [November 1, 2021, 4:16pm UTC](https://discourse.julialang.org/t/how-to-test-if-one-float-is-an-integer-multiple-of-another/70745/3 "2021-11-01T16:16:46Z")

</div>

The moment you represent your numbers in floating point, it’s already too late. The number 1/10 cannot be represented in binary floating point with any finite precision for the same reason that 1/3 cannot be represented in any finite precision decimal value (they’re both just infinitely repeating fractions in their respective bases).

You can use `Rational` numbers, which will give you the exact right answer.

But if you’re somehow stuck with floating-point inputs, then you’re going to have to make up your own tolerances. For example, you could check something like:

```julia
julia> check(a, b) = isapprox(round(b / a) * a, b)
check (generic function with 1 method)

julia> check(0.1, 0.2)
true

julia> check(0.1, 0.25)
false

julia> check(0.1, 0.3)
true

```

Of course, this has edge cases too:

```julia
julia> check(0.1, 0.0) # should be true, and is
true

julia> check(0.1, 1e-16) # what should this be? Not obvious...
false

julia> check(0.1 + 1e-16, 0.2) # seems like this should match the one above...
true

```

What is preventing you from taking exact rational inputs if you actually want exact numerical results here?

---

_[View the full topic](https://discourse.julialang.org/t/how-to-test-if-one-float-is-an-integer-multiple-of-another/70745)._