Question

The decimal representation of `71/150` is ______.

Options

• a terminating decimal

• a nonterminating, repeating decimal

• a nonterminating and nonrepeating decimal

• none of these

Answer 1

The decimal representation of `71/150` is a nonterminating, repeating decimal.

Explanation:

In lowest terms `71/150` has denominator 150 = 2 × 3 × 5². Because the denominator contains a prime factor 3 (not only 2s and 5s), its decimal expansion does not terminate and must repeat; in fact `71/150 = 0.473333`....