Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction.
0.523523... = what fraction?
To change the repeating decimal 0.523523... to a fraction or ratio, follow these steps:
1. Assign a variable, let's say x, to the repeating decimal: x = 0.523523...
2. Multiply both sides of the equation by a power of 10 that will eliminate the repeating part. In this case, we will multiply by 1000 (10^3) since there are three digits repeating. 1000x = 523.523...
3. Subtract the original equation (step 1) from the equation obtained in step 2 to eliminate the repeating part:
1000x - x = 523.523... - 0.523523...
Simplifying this, we get:
999x = 523
4. Divide both sides of the equation by 999 to solve for x:
x = 523 / 999
5. Simplify the fraction. In this case, the numerator and denominator do not share any common factors other than 1, so the fraction is already in its simplest form.
Therefore, the fraction equivalent to the repeating decimal 0.523523... is 523/999.