Write the following infinite decimal expansion as a fraction. You do not need to simplify
0.31 repeated
Let x = 0.31 repeated.
Multiplying both sides by 100, we get:
100x = 31.31 repeated.
Subtracting x from 100x, we get:
99x = 31.
Dividing both sides by 99, we get:
x = 31/99.
Therefore, the infinite decimal expansion 0.31 repeated is equal to the fraction 31/99.