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:
- \( x = 0.2626262626... \)
- \( 100x = 26.2626262626... \)
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
1 answer