Question

Change the decimal to a fraction: 0.2626262626...

Responses:

26 over 99

2 and 6 over 10

26 and 26 over 100

26 over 100

Cannot be written as a fraction

Answer 1

To convert the repeating decimal \( 0.2626262626... \) to a fraction, we can set \( x = 0.262626... \).

1. First, multiply both sides by 100 to shift the decimal point two places to the right:
\[
100x = 26.262626...
\]

2. Next, subtract the original \( x \) from this equation:
\[
100x - x = 26.262626... - 0.262626...
\]
This simplifies to:
\[
99x = 26
\]

3. Now, solve for \( x \):
\[
x = \frac{26}{99}
\]

Thus, the repeating decimal \( 0.2626262626... \) can be expressed as the fraction \( \frac{26}{99} \).

Therefore, the correct response is:
**26 over 99.**