Question

NEED HELP PLEASE!!! Please explain your answer!

Answer 1

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.
`0.\overline{36}`=0.363636363636...
ok, lets say

`x=0.363636363636`
multiply it by 10^n where n=number of places that repeats
in this case it's n=2 so 10^2=100

`100x=36.36363636363636`

now do

`100x-x=36.3636363636-0.3636363636`
the repeating parts cancle leaviing us with

`99x=36`
x=the number
divide both sides by 99

`x=(36)/(99)`

`x=(4)/(11)`

so

`0.\overline{36}=(4)/(11)`



b.
`0.3\overline{6}`
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

`x=(0.6)/(9)`



`x=(2)/(30)`

so
0.36666666666=




c.
`0.36=(.36)/(1)=(3.6)/(10)=(36)/(100)=(9)/(25)`











so
1.
a.
`0.\overline{36}=(4)/(11)`
b.
`0.3\overline{6}=(11)/(30)`
c.
`0.36=(9)/(25)`

Answer 2

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