Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.523523.... = what fraction?
-1000x=523.523523
-subtract 1x = 0.523523
-999x=523
-x = 523/999
-let x = 0.523523
1. Let x = 0.523523
2. Multiply both sides of the equation by a power of 10 to eliminate the repeating decimal. In this case, multiply by 1000 to get -1000x = 523.523523.
3. Subtract 1x from both sides of the equation to isolate the repeating decimal. This gives -999x = 0.523523.
4. Multiply both sides of the equation by -1 to solve for x. This gives 999x = -0.523523.
5. Divide both sides of the equation by 999 to solve for x. This gives x = -0.523523/999.
6. Simplify the fraction by dividing the numerator and denominator by the greatest common divisor. In this case, the greatest common divisor of 523 and 999 is 1, so the fraction cannot be further simplified.
7. Therefore, the fraction equivalent to the repeating decimal 0.523523 is x = -0.523523/999.