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NEED HELP PLEASE!!! Please explain your answer!

NEED HELP PLEASE!!! Please explain your answer!-example-1

2 Answers

1 vote
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=\frac{6}{90)

x=(2)/(30)

so
0.36666666666=
0.3+(2)/(30)=\frac{9}{30)+(2)/(30)=(11)/(30)



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)
User BoburShox
by
7.7k points
2 votes
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
User Mostsquares
by
7.8k points

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