Question

The decimal expansion of following numbers will terminate after how many places (1) (47)/(200) (i) 359/1250​

Answer 1

Given : (1) (47)/(200) (i) 359/1250​

To Find : The decimal expansion of numbers will terminate after how many places

Solution:

47/200

= 47 /( 2 * 100 )

= 47 * 5 / (2 * 100 * 5)

= 47 * 5 / ( 10 * 100)

= 47 * 5 /1000

= 47 * 5 / 10³

Hence decimal expansion of number  will terminate after   3 decimal places

359/1250​

= 359 / (5 * 5 * 5 * 10)

= 359 * 2 * 2 * 2/ ( 5 * 5 * 5 * 10* 2 * 2 * 2)

= 359 * 2 * 2 * 2/ ( 10* 10* 10 * 10)

= 359 * 2 * 2 * 2/ ( 10000)

= 359 * 2 * 2 * 2 / 10⁴

Hence decimal expansion of number  will terminate after 4 decimal places

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