Question

Change the decimal to a fraction: 0.2626262626...(1 point) Responses 2610 2 and 6 tenths 2699 26 over 99 Cannot be written as a fraction Cannot be written as a fraction 26100 26 over 100 2626100

Answer 1

To convert the repeating decimal \( 0.262626... \) (where "26" repeats) into a fraction, we can use the following steps:

1. Let \( x = 0.262626... \).
2. To eliminate the repeating part, multiply \( x \) by 100 (two places to the right, since "26" has two digits):
\[
100x = 26.262626...
\]
3. Now we have two equations:
\[
x = 0.262626...
\]
\[
100x = 26.262626...
\]
4. Subtract the first equation from the second:
\[
100x - x = 26.262626... - 0.262626...
\]
\[
99x = 26
\]
5. Now solve for \( x \):
\[
x = \frac{26}{99}
\]

Thus, the fraction representation of \( 0.262626... \) is \( \frac{26}{99} \).

So, the correct response is **26 over 99**.