Question

the decimal expansion of the no. 16/625 will terminate after how many decimal places

Answer 1

Answer:

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Step-by-step explanation:

4 places

The factors of the denominator 625 is 5⁴ × 2^0. So it has a terminating decimal expansion. It will terminate after 4 places of decimal.

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...

Answer 2

16/625= 0.0256

it will terminate after 4 decimal places