0.05 repeating 5

Question

What is the fraction for the decimal expansion above?

Answer 1

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.