Question

Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747... = what fraction? (5 points)

99x = 47

Subtract x = 0.474747...

100x = 47.474747...

x = 0.47474747...

x = 47/99

Answer 1

1. Set up an equation by multiplying the repeating decimal by a power of 10 to shift the decimal point. In this case, multiply by 100 to get rid of the repeating part.

2. Subtract the original equation from the new equation to eliminate the repeating part. In this case, subtract 47 from 47.474747...

3. Solve for x by dividing both sides by the coefficient of x, which is 100 in this case.

4. Simplify the resulting fraction, if possible, by finding the greatest common divisor of the numerator and denominator and dividing both by that.

The fraction corresponding to the repeating decimal 0.474747... is 47/99.