Put the steps to change the repeating decimal, which is rational, to a ratio or fraction.
0.523523. = what fraction?
(5 points)
Let x = 0.523523...
1000x523.523523...
999x = 523
Subtract 1x = 0.523523...
X = 523 999
To change the repeating decimal 0.523523... to a fraction, follow these steps:
1. Let x be equal to the repeating decimal: x = 0.523523...
2. Multiply both sides of the equation by 1000 to eliminate the repeating part: 1000x = 523.523523...
3. Subtract x from both sides of the equation to isolate the repeating part on the right side: 1000x - x = 523.523523... - 0.523523...
4. Simplify the equation: 999x = 523
5. Divide both sides of the equation by 999 to isolate x: x = 523/999
Therefore, the fraction equivalent of the repeating decimal 0.523523... is 523/999.