Question

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

2 6/10
2 and 6 tenths

26/100
26 over 100

2699
26 over 99

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

26 26/100

Answer 1

To convert the decimal 0.2626262626... (which can be expressed as \(0.\overline{26}\)) into a fraction, we can set up an equation:

Let \( x = 0.\overline{26} \).

Then, multiplying both sides by 100 (to move the decimal two places to the right), we get:

\[
100x = 26.\overline{26}
\]

Now, we can subtract the original \( x \) from this equation:

\[
100x - x = 26.\overline{26} - 0.\overline{26}
\]

This simplifies to:

\[
99x = 26
\]

Now, solving for \( x \):

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

Thus, the correct response is:

**26/99** or **26 over 99**.