Repeating Decimal to Fraction Conversion

x is what we don’t know … but it will be the fraction whose decimal equivalent is point-seven repeating.

Since the decimal begins repeating at the 10ths place, we will multiply both sides by 10.

Subtract your first equation from the second. Now just divide to solve for x.

x is what we don’t know … but it will be the fraction whose decimal equivalent is point-five three repeating.

This time we multiply by 100, because the decimal repeats to the 100ths place.

Subtract the first from the second.

This is trickier because we want to get the repeating decimal to begin immediately after the decimal point.

Subtract the 1st equation from the 2nd. First equation! Now multiply by 1,000 because that’s how far .173 repeats, to the thousandths place. So we are going to multiply by 100 to our first equation before doing anything else. Now just divide to solve for x. Reduce by 4