Question

show how 11 divided by 2 power 3× 5 will have terminating or non terminating decimal expansion​

Answer 1

Answer:

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.