I really need help, these equations aren't making sense.?

Question

I've been sitting here for the past 10 minutes looking at these problems and trying to solve them and I'm just completely stuck.

I have to take these repeating decimals and turn them into a fraction or mixed number.

The decimals:
__
-1.36
___
- 2.707

I know the answers. Thats not what I'm interested in. I want to know HOW to get that, I honestly can't figure it out.

The answers are: - 1 4/11 and the second one is 2 707/999


Help PLEASE.

Aghhh.

The line above the first one should be over the .36 and the line above the second one should be over the 707. Sorry about that, it messed up.

Answer 1

basically you just pay attention to the part that repeats...so for -1.36, the 36 is the only part that repeats... so make a variable and assign it some of the repeating part .36:
a = .36363636363636....
ok so now we can can multiply this by 10, 100, etc:
10a = 3.63636363....
100a = 36.3636363 ....
all we did was change part to non decimal
ok so now that we have the repeating part in the non-decimal portion of our number (ie. 100a), you can subtract a from 100a:

100a = 36.363636363...
- a = 0.363636363...
----------------------------------
99a = 36.0

now just solve for a
a = 36/99
you can simplify this to 12/33 (dividing denominator and numerator by 3)
and so 13/33 is the repeating part...now just put back the -1 that we took away at the start and you get -1 4/11 or -15/11 if you want a non mixed fraction.

Answer 2

ok what you do is put 36/100 and simplify it to 9/25, then kind of guess and check on the calculater with similar fractions until you get one that end up being .36 repeding