0.05 repeating 5
What is the fraction for the decimal expansion above?
To find the fraction for the decimal expansion, let x = 0.05 repeating 5.
We can multiply both sides of the equation by 100 (since there are 2 decimal places) to eliminate the decimal:
100x = 5.555...
Now, subtract the original equation from the new equation:
100x - x = 5.555... - 0.055...
Simplifying the equation:
99x = 5.5
Dividing both sides by 99:
x = 5.5/99
Therefore, the fraction for the decimal expansion 0.05 repeating 5 is 5.5/99.