Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction.
0.523523…= what fraction?
1. Let x represent the repeating decimal (0.523523...).
2. Multiply x by a power of 10 that shifts the repeating part to the left of the decimal point. In this case, multiplying by 1000 is appropriate since there are 3 digits in the repeating part.
x = 0.523523...
1000x = 523.523523...
3. Subtract the original number from the result.
1000x - x = 523.523523... - 0.523523...
= 523
Simplifying: 999x = 523
4. Solve the equation for x.
x = 523/999
Therefore, the fraction representation of the repeating decimal 0.523523... is 523/999.