Change the decimal to a fraction: 0.2626262626

A. 2 6/10
B. Cannot be written as a fraction
C. 26/100
D. 26 26/100
E. 26/99

1 answer

The decimal 0.2626262626 is a repeating decimal (0.26 with the "26" repeating). To convert it to a fraction, we can use the following method:

Let \( x = 0.262626...\)

To eliminate the repeating part, we can multiply both sides by 100 (since the repeating block has 2 digits):

\[ 100x = 26.262626... \]

Now we can set up an equation by subtracting the original \( x = 0.262626...\) from this new equation:

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

This simplifies to:

\[ 99x = 26 \]

Now, solving for \( x \):

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

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

Thus, the correct answer is:

E. 26/99