# How to check the rationality of a number? [closed]

A rational number is a number that can be written in the form $\frac{a}{b}$ where $b\neq 0$, I'm doing an exercise where the author asks: Is 5.96 a rational number?

I believe I should find one $a$ and one $b$ such that $\frac{a}{b}=5.96$ to prove it's rational, but I don't know how to search for these numbers, can you help me?

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## closed as too localized by Amr, TMM, Davide Giraudo, Nameless, FabianDec 29 '12 at 14:48

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Try 596/100 - and cancel it if you wish. More generally, any terminating decimal is a rational, and you can get a fraction $a/b$ by multiplying by a sufficiently large power of 10. –  Old John Dec 29 '12 at 13:43
Got it. Thanks. –  Vÿska Dec 29 '12 at 13:47

Note that if $x=5.96$ then $100x=596$.
Your question would be better if you asked: Why $5.9696969696...$ is a rational. Yes as @Amr and dear Old john suggested as well, you need to do that. :) –  Babak S. Dec 29 '12 at 13:50
$$\\\\\\\\\\\\\\\\\\5.96=\frac{596}{100}$$