Convert the decimal expansion 0.31717 to a fraction. a) 133/455 b) 157/495 c) 52/165 d) 99/166

The decimal expansion of 0.31717 is an infinite number with the 17 repeating.

Let the given decimal = X, so we have X = 0.31717 ( 1st equation)

Multiply both sides by 100 to get:
100x = 31.717 ( 2nd equation)

Subtract the 1st equation from the 2nd equation:

100x = 31.1717 - x = 0.31717 = 99x = 31.4

Divide both sides by 99:
X = 31.4 / 99

Multiply both numbers by 10 to remove the decimal point:
X = 314 / 990

Divide both numbers by 2 to get the final answer of 157 / 495

The answer is B.