# Is 0.99999999 a rational, irrational number, natural, whole or integer?

Jun 30, 2015

If it stops after 8 decimal places then it is a rational number,

equal to $\frac{99999999}{100000000}$.

If it is a an infinitely recurring patten of $9$'s, then it is equal to $1$.

#### Explanation:

A rational number is any number that can be expressed as $\frac{p}{q}$ for some integers $p$ and $q$, with $q \ne 0$.

$1$ is a rational number, being equal to $\frac{1}{1}$. It is also a natural number, whole and integer.

If you are familiar with the 'dot' notation for recurring decimals, then you can write:

$0. \dot{9} = 1.0$

If you are not sure this is so, try subtracting:

$1.0 - 0. \dot{9}$

and see that you get $0. \dot{0} = 0$