Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction.
0.523523... = what fraction?
1 x=523/999
2 999x=523
3 1000x=523.523523...
4 let x = 0.523523.....
5 subtract 1x=0.52353..
1. Let x = 0.523523...
2. Multiply both sides of the equation by 1000 to eliminate the decimal places: 1000x = 523.523523...
3. Subtract the original equation (step 1) from the equation in step 2: 1000x - x = 523.523523... - 0.523523...
4. Simplify the equation: 999x = 523
5. Divide both sides of the equation by 999 to solve for x: x = 523/999
Thus, the fraction equivalent of the repeating decimal 0.523523... is 523/999.
whats the seconded answer
I apologize for the confusion earlier. Here is the correct order of steps for changing the repeating decimal 0.523523... to a fraction:
1. Let x = 0.523523...
2. Multiply both sides of the equation by 1000 to eliminate the decimal places: 1000x = 523.523523...
3. Let y = 0.523523... (to represent the repeating part)
4. Multiply both sides of the equation by 1000 again: 1000y = 523.523523...
5. Subtract the equation in step 3 from the equation in step 4:
1000y - y = 523.523523... - 0.523523...
6. Simplify the equation: 999y = 523
7. Divide both sides of the equation by 999 to solve for y: y = 523/999
Since we let y represent the repeating part, the fraction equivalent of the repeating decimal 0.523523... is 523/999.