Question

Find after how many digits will the decimal expansion of 147/120 terminate

Answer 1

the decimal expansion of 147/120 will terminate after 3 decimal places

Answer 2

After 3 decimal places.

Because,

q = 120

$= 60 \times 2 \\ = 30 \times 2 \times 2 \\ = 3 \times 10 \times 2 \times 2 \\ = 2 \times 2 \times 2 \times 5 \times 3 \\ = {2}^{3} \times 3 \times 5$

Highest exponent in the denominator is 3.

Hence, it terminates after 3 decimal places.