Question

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

26 26/100
26 and 26 over 100

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

26/100
26 over 100

26/99
26 over 99

2 6/10

Answer 1

The decimal 0.2626262626... is a repeating decimal, which can be written as a fraction.

To convert it to a fraction, let's denote the repeating decimal as \( x \):

\[
x = 0.2626262626...
\]

To eliminate the repeating part, we can multiply \( x \) by 100 (since the repeating part is two digits long):

\[
100x = 26.2626262626...
\]

Now we have two equations:

1. \( x = 0.2626262626... \)
2. \( 100x = 26.2626262626... \)

Next, we subtract the first equation from the second:

\[
100x - x = 26.2626262626... - 0.2626262626...
\]
\[
99x = 26
\]

Now, we can solve for \( x \):

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

So the repeating decimal 0.2626262626... can be expressed as \( \frac{26}{99} \).

The correct response is:

**26/99**