Question

Change the decimal to a fraction: 0.2626262626..
Cannot be written as a fraction
2음
26
99
• 26 26
100
• 26.
100

Answer 1

To convert the repeating decimal \(0.262626...\) into a fraction, we can use a method involving algebra.

Let \(x = 0.262626...\).

To eliminate the repeating part, we can multiply both sides of the equation by 100. This shifts the decimal point two places to the right:

\(100x = 26.262626...\)

Now, we have two equations:

1. \(x = 0.262626...\)
2. \(100x = 26.262626...\)

Next, we can subtract the first equation from the second:

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

This simplifies to:

\[
99x = 26
\]

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

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

Thus, the decimal \(0.262626...\) can be expressed as the fraction \(\frac{26}{99}\).