Question

what is 0.96 in the simplest form as a fraction (96 repeats)

Answer 1

To convert the repeating decimal \(0.969696...\) (where 96 repeats) into a fraction, we can follow these steps:

1. Let \(x = 0.969696...\).

2. To eliminate the repeating part, we can multiply \(x\) by 100 (since the repeating part has two digits):
\[
100x = 96.969696...
\]

3. Now, we can set up the equation:
\[
100x = 96.969696...
\]
\[
x = 0.969696...
\]

4. Next, we subtract the second equation from the first:
\[
100x - x = 96.969696... - 0.969696...
\]
\[
99x = 96
\]

5. Now, we solve for \(x\):
\[
x = \frac{96}{99}
\]

6. To simplify \(\frac{96}{99}\), we find the greatest common divisor (GCD) of 96 and 99. The GCD is 3, so we divide both the numerator and the denominator by 3:
\[
\frac{96 \div 3}{99 \div 3} = \frac{32}{33}
\]

Therefore, \(0.969696...\) in simplest form as a fraction is \(\frac{32}{33}\).