What is the rational number equivalent to 3 point 24 with a bar over 24?

Question

joehoffy · Answer

3 and 6 over 97
 3 and 28 over 99
 3 and 8 over 33
 3 and 10 over 32

openstudier · Answer

Anytime we have a repeating decimal (what the bar over the number means), we take the repeating part and put it over 9s.
For example:
.222... = 2/9
.252525... = 25/99
.243243243... = 243/999

joehoffy · Answer

okay and?

openstudier · Answer

So, I want you to think about it. You are asking what is 3.242424... as a fraction. By what I said, this means the fraction should be 3 and 24/99, right?

openstudier · Answer

So, 3 and 24/99 reduces down to 3 and 8/33.

joehoffy · Answer

correct...

joehoffy · Answer

@OpenStudier

joehoffy · Answer

but i dont rlly get it.

openstudier · Answer

It's just one of those things that you have to memorize. Just remember that repeating decimals have 9s as the denominator, and the number of 9s depends on the number of digits in the repeating part of the decimal.

joehoffy · Answer

do you have any idea which answer it could be? i really need help and i gave u alot of medals can u please?

zarkon · Answer

let $x=3.\overline{24}$

then $100x=324.\overline{24}$

subtract
$100x=324.\overline{24}$
-    $x=3.\overline{24}$

$99x=321$

$x=\dfrac{321}{99}=3+\dfrac{8}{33}$

openstudier · Answer

I just showed how to get the answer... and I even posted the answer itself above. It's 3 and 8/33, and thank you @Zarkon for showing that proof!

joehoffy · Answer

yes i do thank you

openstudier · Answer

No problem!