Question

49 / 500 without performing long division, state whether it will terminating or non- terminating.

(ii) After how many places of decimal will it terminate. (iii) calculate in decimal form.​

Answer 1

Given : 49 / 500

To Find : without performing long division, state whether it will terminating or non- terminating.

(ii) After how many places of decimal will it terminate.

(iii) calculate in decimal form.​

Solution:

49 / 500

= 7 * 7 / ( 2 * 2 * 5 * 5 * 5 )

=  7 * 7 / ( 2² * 5³)

Denominator has only prime factors of 2 and 5

Hence  it will be  terminating

in 2 and 5  maximum power is 3

Hence it will terminate after 3 decimal place

Multiply numerator and denominator by 2

 7 * 7 *2 / ( 2² * 5³ * 2)

= 98/(2³ * 5³ )

= 98/10³

= 98/1000

= 0.098

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