Question

Convert the following repeating decimal to a fraction in simplest form.
.96 ̅

Answer 1

To convert the repeating decimal .96̅ to a fraction, let's call the decimal x.

We can multiply x by 100 to eliminate the repeating decimal:

100x = 96.96̅

Next, we subtract x from 100x:

100x - x = 96.96̅ - .96̅

This simplifies to:

99x = 96

To isolate x, we divide both sides of the equation by 99:

x = 96 / 99

The fraction 96/99 can be simplified by finding the greatest common divisor (GCD) of 96 and 99, which is 3:

96 / 99 = (96 / 3) / (99 / 3) = 32 / 33

Therefore, the fraction equivalent to the repeating decimal .96̅ is 32/33 in simplest form.