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animecreep447
              You must make it a fraction by multiplying by 100, moving the decimal over by 2 spaces right so we have 36. Then, put it over 100, because it is a fraction. Now, with 36/100 we must simplify by dividing each number by another # that goes into it evenly, such as 2. We get 18/50, reduce by 2, we get 9/25. There you go hope I helped 
apologiabiology
if something repeats, it's probably divided by 9 or 99 or 999 or however many places repeats
but I'll show how to solve


1.
a. [tex]0.\overline{36}[/tex]=0.363636363636...
ok, lets say
[tex]x=0.363636363636[/tex]
multiply it by 10^n where n=number of places that repeats
in this case it's n=2 so 10^2=100
[tex]100x=36.36363636363636[/tex]

now do
[tex]100x-x=36.3636363636-0.3636363636[/tex]
the repeating parts cancle leaviing us with
[tex]99x=36[/tex]
x=the number
divide both sides by 99
[tex]x=\frac{36}{99}[/tex]
[tex]x=\frac{4}{11}[/tex]

so
[tex]0.\overline{36}=\frac{4}{11}[/tex]



b. [tex]0.3\overline{6}[/tex]
0.3666666666666666666=0.3+0.0666666666666666
let's find what 0.06666666666 is as a fraction
x=0.0666666666666
how many spaces repeat? 1
times it by 10
10x=0.666666666666666666
minus them, do 10x-x
10x-x=0.66666666666666-0.0666666666666666
9x=0.6
divide by 9
[tex]x=\frac{0.6}{9}[/tex]
[tex]x=\frac{6}{90)[/tex]
[tex]x=\frac{2}{30}[/tex]

so
0.36666666666=[tex]0.3+\frac{2}{30}=\frac{9}{30)+\frac{2}{30}=\frac{11}{30}[/tex]



c. [tex]0.36=\frac{.36}{1}=\frac{3.6}{10}=\frac{36}{100}=\frac{9}{25}[/tex]











so
1.
a. [tex]0.\overline{36}=\frac{4}{11}[/tex]
b. [tex]0.3\overline{6}=\frac{11}{30}[/tex]
c. [tex]0.36=\frac{9}{25}[/tex]

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