1
$\begingroup$

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?

  • 3
    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 10.2012-12-29
  • 0
    Got it. Thanks.2012-12-29

2 Answers 2

4

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

  • 0
    But I need only to divide by 100?2012-12-29
  • 0
    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. :)2012-12-29
  • 0
    Helpful answer +12013-03-01
2

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