Show me step by step how to convert a repeating decimal 3.152 into a improper fraction or mixed number

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
Step 1. There are 3 repeating digits
Step 2. The multiplier is . The multiplied number is
 
Step 3. Subtract the original number
 
Step 4. Divide by 1000 - 1 = 999
 
This fraction does not reduce, so you are done.

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