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:

3.{152} = 3 152/999

Step-by-step explanation:

Let X equal the decimal number

Equation 1:

X=3.{152}     ...(1)

With 3 digits in the repeating decimal group,

create a second equation by multiplying

both sides by 103 = 1000

Equation 2:

1000X=3152.{152}   ...(2)

Subtract equation (1) from equation (2)

1000X=3152.{152}

X=3.{152}

We get

999X=3149

Solve for X

X=3149/999

Simplify the improper fraction,

=3 152/999

In conclusion,

3.{152}=3 152/999