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

Question

Responses

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

2626100
26 and 26 over 100

26100
26 over 100

2610
2 and 6 tenths

2699

Answer 1

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

1. Let \(x = 0.262626...\).
2. Multiply both sides by 100 (since the decimal repeats every 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. Solving for \(x\): \[ x = \frac{26}{99} \]

So the fraction that represents \(0.2626262626...\) is \(\frac{26}{99}\).

None of the provided responses correctly match \(\frac{26}{99}\).