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

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Answer 1 · 2015-06-30T22:00:57

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

equal to $99999999/100000000$ .

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

A rational number is any number that can be expressed as $p/q$ for some integers $p$ and $q$ , with $q != 0$ .

$1$ is a rational number, being equal to $1/1$ . 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 $0.dot(0) = 0$

Is 0.999999990.99999999 a rational, irrational number, natural, whole or integer?