Converting 2.5 Repeating to a Fraction: A Step-by-Step Guide

To convert the repeating decimal 2.5 (where the digit 5 repeats indefinitely) into a fraction, we can follow these steps:

1. Define the repeating decimal: Let's represent the repeating decimal as x:

   x = 2.55555...

2. Multiply to eliminate the repeating part: To isolate the repeating decimal, we multiply both sides of the equation by 10:

   10x = 25.55555...

3. Set up an equation: Now, we have:

         10x = 25.55555...
         x = 2.55555...
       

   Next, we subtract the second equation from the first:

4. Subtract the equations:

         10x - x = 25.55555... - 2.55555...
         9x = 23
       

5. Solve for x: Now, divide both sides by 9:

         x = 23/9
       

6. Conclusion: Therefore, the repeating decimal 2.5 can be expressed as the fraction 23/9.

And that's how you convert 2.5 repeating into a fraction!