Convert the decimal expansion 0.31717 to a fraction. A) 133/455 B) 157/495 C) 52/165 D) 99/166
1 answer:
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.
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