Question

Change the decimal to a fraction: 0.2626262626...(1 point)
Responses

2610
2 and 6 tenths

26100
26 over 100

Cannot be written as a fraction
Cannot be written as a fraction

2699
26 over 99

2626100
26 and 26 over 100
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Answer 1

To convert the repeating decimal \(0.2626262626...\) into a fraction, we can follow these steps:

Let \(x = 0.262626...\).

To eliminate the repeating part, we can multiply by 100 (because the repeating part "26" has two digits):

\[
100x = 26.262626...
\]

Now we have two equations:
1. \(x = 0.262626...\)
2. \(100x = 26.262626...\)

Next, we subtract the first equation from the second:

\[
100x - x = 26.262626... - 0.262626...
\]
\[
99x = 26
\]

Now, divide both sides by 99:

\[
x = \frac{26}{99}
\]

Thus, the repeating decimal \(0.2626262626...\) as a fraction is \(\frac{26}{99}\).

The correct response is:

**2699: 26 over 99.**