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 be the repeating decimal, in this case, x = 0.523523...
2) Multiply both sides of the equation x = 0.523523... by a power of 10 to shift the repeating part to the left of the decimal point. Since there are three digits in the repeating part (523), multiply by 1000: 1000x = 523.523523...
3) Subtract x from both sides of the equation to eliminate the repeating part: 1000x - x = 523.523523... - 0.523523...
Simplifying, we get: 999x = 523
4) Divide both sides of the equation by 999 to solve for x: x = 523/999
5) To simplify the fraction 523/999, find the greatest common divisor (GCD) of the numerator and denominator, and divide both by it to get the simplest form. In this case, the GCD of 523 and 999 is 1. Hence, the fraction is already in its simplest form, and the ratio of the repeating decimal 0.523523... is 523/999.