Change the repeating decimal 0.453453453…. into a fraction.

Question

Change the repeating decimal 0.453453453…. into a fraction.

Answer 1

1: Let x = .453453453453453...

2: Rewrite statement so the one of the repeating portions is moved to left of decimal. In this case, multiply both sides of equation by 1000

3: Write new equation. 1000x = 453.453453453453...

4: Subtract the two equations: 1000x = 453.453453453...

- x = .453453453453...

5: Solve new equation: 999x = 453

Thus x = 453/999

Answer 2

Quick trick: Put the repeating unit decimal over that number of nines with the same number of digits.

.88888... = 8/9

.121212... = 12/99

.413413.... = 413/999

also, .09191... is 1/10 * 91/99 or 91/990