Step 1. Count the number of repeating digits.
Step 2. Multiply the number by 10 to that power.
Step 3. From that product, subtract the original number.
Step 4. Divide the result by 1 less than the multiplier of Step 2.
Step 5, Reduce the fraction.
For your number [tex]3. \overline{152}[/tex]
Step 1. There are 3 repeating digits
Step 2. The multiplier is [tex]10^{3}=1000[/tex]. The multiplied number is
[tex]1000 \cdot 3. \overline{152}=3152. \overline{152}[/tex]
Step 3. Subtract the original number
[tex]3152. \overline{152}-3. \overline{152}=3149[/tex]
Step 4. Divide by 1000 - 1 = 999
[tex]\dfrac{3149}{999}=3 \frac{152}{999}[/tex]
This fraction does not reduce, so you are done.
