Question

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

Answer 1

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

Answer 2

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 = 3.152152

• Since, it is to 3 decimal places : multiply both sides by 10³

• 10³ = 10 × 10 × 10 = 1000

• 1000 × x = 3.152152 × 1000

• 1000x = 3152.152 - - - (2)

Subtract (1) from (2)

• 1000x - x = 3152.152- 3.152

• 999x = 3149

• Divide both sides by 999

• 999x/999 = 3149/999

• x = 3149 / 999

• x = 3149 /999 = 3 152/999

Hence, 3.152 in fraction is 3149/999

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