Convert the repeating decimal to an improper fraction or mixed number. include your work in your final answer. 3.152

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

The value 3.152 expresses as a fraction is 3149 / 999

Given the decimal : 3.152

To convert to fraction :

Represent the decimal as x x = 3.152 ---(1)Actual repeating decimal = 3.152152Since, it is to 3 decimal places : multiply both sides by 10³10³ = 10 × 10 × 10 = 10001000 × x = 3.152152 × 10001000x = 3152.152 - - - (2)

Subtract (1) from (2)

1000x - x = 3152.152- 3.152999x = 3149Divide both sides by 999999x/999 = 3149/999x = 3149 / 999x = 3149 /999 = 3 152/999

Hence, 3.152 in fraction is 3149/999

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221,500 is the answer