Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction.
0.523523... = what fraction?
x=523/999
999x=523
1000x=523.523523...
let x = 0.523523.....
subtract 1x=0.52353...
1. Let x = 0.523523...
2. Multiply both sides of the equation by 1000 to shift the decimal point to the right.
3. 1000x = 523.523523...
4. Subtract 1x = 0.523523... from 1000x = 523.523523...
5. Simplify the equation to 999x = 523
6. Solve for x by dividing both sides of the equation by 999
7. x = 523/999
So, the fraction equivalent to the repeating decimal 0.523523... is 523/999.