Question

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
subtract 1x =0.523523
999x = 523
1000x = 523.523523
Let x =0.523523

Answer 1

1. Let x = 0.523523...
2. Multiply both sides of the equation by 1000 to remove the decimal: 1000x = 523.523523...
3. Subtract x from both sides of the equation: 999x = 523.523523... - 0.523523...
4. Simplify the right side of the equation: 999x = 523
5. Divide both sides of the equation by 999 to solve for x: x = 523/999
The fraction equivalent of the repeating decimal 0.523523... is 523/999.