Question

is 686/19600 terminating? if so many decimal places it will terminate

Answer 1

hope this helps you....

Answer 2

Solution :-

686/19600

686 = 2*7*7*7 = 2 × 7³

19600 = 2*2*2*2*5*5*7*7 = 2⁴ × 5² × 7²

⇒ (2 × 7³)/(2⁴ × 5² × 7²) 

⇒ (7¹)/(2³ × 5²)

⇒ (7)/(2 × 2 × 2 × 5 × 5)

⇒ (7 × 5)/(2 × 2 × 2 × 5 × 5 × 5)

⇒ 35/1000

= 0.035

Therefore, the decimal expansion of 686/19600 will terminate after 3 decimal places.

Answer.