How to check the rationality of a number?

Question

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?

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

score 4 · Accepted Answer · answered Dec 29 '12 at 13:45

4

Note that if $x=5.96$ then $100x=596$.

answered Dec 29 '12 at 13:45

Mikasa

67,374

But I need only to divide by 100? – Red Banana Dec 29 '12 at 13:45
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. :) – Mikasa Dec 29 '12 at 13:50
Helpful answer +1 – amWhy Mar 01 '13 at 00:59

score 2 · Answer 2 · answered Dec 29 '12 at 13:46

2

$$\\\\\\\\\\\\\\\\\\5.96=\frac{596}{100}$$

answered Dec 29 '12 at 13:46

Amr

20,030

How to check the rationality of a number?

2 Answers2