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