Question

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

2610
2 and 6 tenths

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

2699
26 over 99

26100
26 over 100

2626100

Answer 1

To convert the repeating decimal \(0.2626262626...\) into a fraction, you can use the following method:

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

This decimal can be expressed as:
- Multiply both sides by 100 (because the repeating part is two digits long):

\(100x = 26.262626...\)

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

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 decimal \(0.262626...\) can be expressed as the fraction \(\frac{26}{99}\).

From the provided options, the correct answer is:

**26 over 99.**