Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.523523.... = what fraction?(5 points)
1. Let x be the repeating decimal, in this case 0.523523...
2. Multiply both sides of the equation by a power of 10 in order to move the decimal point to eliminate the repeating part. In this case, we can multiply by 1000 since there are 3 digits in the repeating part.
1000x = 523.523...
3. Subtract the original equation from the multiplied equation to eliminate the repeating part.
1000x - x = 523.523... - 0.523...
Simplifying gives: 999x = 523
4. Divide both sides of the equation by 999 to isolate x.
x = 523/999
5. Simplify the fraction if possible. In this case, the numerator and denominator can be divided by their greatest common divisor, which is 1.
x = 523/999 is already simplified.
Therefore, the fraction equivalent to the repeating decimal 0.523523... is 523/999.