Question

The decimal expansion of the rational number 15/6400

will terminate after how many places of

decimals, and hence find the decimal expansion without doing long division​

Answer 1

8 places if it is wrong sorry if correct mark brilliant

Answer 2

Given :  15/6400

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

decimals

Solution:

15/6400

= 3 * 5 / 6400

= 3/ 1280

= 3/ ( 10 * 128 )

= 3/ (10 * 2⁷)

= 3 * 5⁷ / ( 10 * 2⁷ * 5⁷)

= 3 * 5⁷/ ( 10 * 10⁷)

= 3 * 5⁷/ (10⁸)

Hence The decimal expansion  will terminate after how 8  places of

decimals

15/6400 = 2,34,375/10⁸

0.00234375

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