Question

Convert the repeating decimal to an improper fraction or mixed number. Include your work in your final answer. \(3.\overline{152}\)

Answer 1

Answer:

Assuming the repetitive part is 152, i.e. the original repeating decimal is

A=3.152152152....

then  

1000A=3152.152152152152....

subtract A

1000A-A=3152.152152....-3.152152152....

999A=3149

A=3149/999=3+152/999=3 152/999

Therefore

3.152152152.... = 3149/999 or 3 152/999