Question

The decimal expansion of the rational number `17/160` will terminate after ______ decimal places.

Options

• 1

• 2

• 4

• 5

Answer 1

The decimal expansion of the rational number `17/160` will terminate after 5 decimal places.

Explanation:

The rational number given is `17/160`.

To determine the number of decimal places where the decimal expansion will terminate, we factorise the denominator 160 = 2⁵ × 5¹.

Since the denominator is of the form 2^m × 5ⁿ where m = 5 and n = 1 both whole numbers, the decimal expansion of the rational number will be terminating.

The number of decimal places in the terminating decimal expansion is the maximum of m and n, which is max(5, 1) = 5.

Therefore, the decimal expansion of `17/160` will terminate after 5 decimal places.