Convert the following repeating decimal to a fraction in simplest form. .91 with 1 repeating

Answer 1

To convert the repeating decimal .91 to a fraction, we can set up the equation x = .91 + .01x, because the decimal repeats the 1 indefinitely.

Multiplying both sides by 100 (to move the decimal place two places to the right) gives us:

100x = 91 + 1x.

Combining like terms, we get:

99x = 91.

Dividing both sides by 99, we find:

x = 91/99.

Therefore, the repeating decimal .91 is equal to the fraction 91/99 in simplest form.