Question

the number of decimal places after which the decimal expansion of the rational number 14588 by 625 will terminate is

Answer 1

after 4 places I hope it will help you

Answer 2

if the factors of denominator of the given rational number is of the form 2ⁿ 5^m , where n and m are nonnegative integers, then the decimal expansion of the decimal number is terminating otherwise non terminating recurring.

Given:

14588/625

The factors of the denominator 625 is 5⁴ × 2^0. So it has a terminating decimal expansion.

Now, 14588/625 = 14588 ×2⁴ / 5⁴ × 2⁴

14588/625 =14588 × 16 / (10)⁴

= 233408/10⁴

= 233408/10000

= 23.3408

It will terminate after 4 places of decimal.

HOPE THIS WILL HELP YOU...