Asked by Landry
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?
Answers
Answered by
Scott
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
... 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
Answered by
Reiny
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
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
Answered by
Reiny
For your case:
0.0833333....
= (83 - 08)/900
= 75/900
= 1/12
check: 1/12 = .08333...
0.0833333....
= (83 - 08)/900
= 75/900
= 1/12
check: 1/12 = .08333...
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.