Question

My homework is converting repeating decimals into fractions. I can't figure out the steps for this problem: 0.083 and the 3 is the repeating number. Can someone please explain the steps to me?

Answer 1

one digit is repeating
... so multiply the number by 10^1

10 n = .8333...

n = .08333...

subtracting ... 9 n = .75 (the 3's cancel)

n = .75 / 9 = (3/4) / 9 = 3 / 36 = 1 / 12

Answer 2

general method:
e.g. .34567567567... (the 567 repeats)

for the numerator:
1. Without the decimal, write down the digits to the end of the first repeat:
-----> 34567
2. From that , subtract all the digits that don't repeat:
---> 34567-34 = 34533

for the denominator:
1. write down a 9 for each of the repeating digits
there are 3 digits repeating, so ---> 999
2. tag on a 0 for each of the non-repeating digits
there are two of those, so ---> 99900

fraction is 34533/99900
or reduced to 3837/11100 = 1279/3700

check with a calculator

another e.g.
.666666....

numerator = 6 - 0 = 6
denominator = 9 , there is a single digit repeating, so one 9, and there are no non-repeating, so no zero has to be tagged on

= 6/9
= 2/3

Answer 3

For your case:
0.0833333....

= (83 - 08)/900
= 75/900
= 1/12

check: 1/12 = .08333...