Question

1. The decimal representation of 1/23x5 will​

Answer 1

QUESTION : The decimal representation of 11/2^3*5 will

a) terminate after 1 decimal place

b) terminate after 2 decimal places

c) terminate after 3 decimal places

d) not terminate​

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ANSWER: option (c) terminate after 3 decimal places.

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EXPLANATION : The decimal representation of 11/(2³ × 5) ;

multiplying and dividing by 5²,

= 11/(2³ × 5) × (5²/5²)

= (11 × 5²)/(2³ × 5 × 5²)

= (11 × 25)/(2³ × 5³)

[ we know, aⁿ × bⁿ = (ab)ⁿ

so, 2³ × 5³ = (2 × 5)³ = (10)³ ]

= (275)/(10³)

= 275/1000

= 0.275

here it is clear that, decimal representation of 11/(2³ × 5) will terminate after 3 decimal places.

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