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