SOLUTION: How to solve : converting a repeating decimal to a fraction 0.83 with only the 3 repeating, and 2.04 with only the .04 repeating.

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Question 394429: How to solve : converting a repeating decimal to a fraction
0.83 with only the 3 repeating, and
2.04 with only the .04 repeating.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
.83 with the 3 repeating
This is .8 + .0333333 etc.
.8+=+4%2F5
I can say:
x+=+.03333333 etc.
10x+=+.333333 etc.
10x+-+x+=+.3333333+-+.0333333 (infinitely many 3's)
9x+=+.3
x+=+.3%2F9
x+=+3%2F90
x+=+1%2F30
4%2F5+%2B+1%2F30+=+24%2F30+%2B+1%2F30
25%2F30+=+5%2F6 answer
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2.040404 with .04 repeating
2+%2B+.040404
x+=+.040404 (.04 repeating)
100x+=+4.040404
100x+-+x+=+4
99x+=+4
x+=+4%2F99
2+%2B+4%2F99+=+198%2F99+%2B+4%2F99
202%2F99 answer