# std::ratio

From cppreference.com
< cpp‎ | numeric‎ | ratio

Defined in header `<ratio>` |  |
template< std::intmax_t Num, std::intmax_t Denom = 1 > class ratio; |  | (since C++11)

The class template `std::ratio` provides compile-time rational arithmetic support. Each instantiation of this template exactly represents any finite rational number as long as its numerator `Num` and denominator `Denom` are representable as compile-time constants of type std::intmax_t. In addition, `Denom` may not be zero and may not be equal to the most negative value. Both numerator and denominator are automatically reduced to the lowest terms.

Several convenience typedefs that correspond to the SI ratios are provided by the standard library:

Defined in header `<ratio>`
Type | Definition
`yocto` | std::ratio<1, 1000000000000000000000000>, if std::intmax_t can represent the denominator
`zepto` | std::ratio<1, 1000000000000000000000>, if std::intmax_t can represent the denominator
`atto` | std::ratio<1, 1000000000000000000>
`femto` | std::ratio<1, 1000000000000000>
`pico` | std::ratio<1, 1000000000000>
`nano` | std::ratio<1, 1000000000>
`micro` | std::ratio<1, 1000000>
`milli` | std::ratio<1, 1000>
`centi` | std::ratio<1, 100>
`deci` | std::ratio<1, 10>
`deca` | std::ratio<10, 1>
`hecto` | std::ratio<100, 1>
`kilo` | std::ratio<1000, 1>
`mega` | std::ratio<1000000, 1>
`giga` | std::ratio<1000000000, 1>
`tera` | std::ratio<1000000000000, 1>
`peta` | std::ratio<1000000000000000, 1>
`exa` | std::ratio<1000000000000000000, 1>
`zetta` | std::ratio<1000000000000000000000, 1>, if std::intmax_t can represent the numerator
`yotta` | std::ratio<1000000000000000000000000, 1>, if std::intmax_t can represent the numerator

### Member types

Member type | Definition
`type` | std::ratio<num, den>

### Member objects

constexpr intmax_t num [static] | constexpr value of type std::intmax_t equal to `sign(Num) * sign(Denom) * abs(Num) / gcd(Num, Denom)` (public static member constant)
constexpr intmax_t den [static] | constexpr value of type std::intmax_t equal to `abs(Denom) / gcd(Num, Denom)` (public static member constant)

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