How do you convert 0.87 (7 repeating) to a fraction?

To convert the repeating decimal 0.87(7) (where 7 repeats indefinitely) into a fraction, follow these steps:

Step 1: Let the repeating decimal be represented as x. So, let: x = 0.877777... (where the 7 repeats).

Step 2: Eliminate the repeating decimal by multiplying both sides of the equation by 10 (to shift the decimal point one place to the right): 10x = 8.77777...

Step 3: Now subtract the original equation (x = 0.87777...) from this new equation (10x = 8.77777...): (10x - x) = (8.77777... - 0.87777...) This simplifies to: 9x = 7.9

Step 4: Solve for x by dividing both sides by 9: x = 7.9 / 9

Step 5: To eliminate the decimal in the numerator, multiply both the numerator and the denominator by 10: x = (7.9 * 10) / (9 * 10) x = 79 / 90

So, 0.87(7) as a fraction is 79/90.