The number of decimal places after which the decimal expansion of the rational number 14588÷625 will terminate is
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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...
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...
Answered by
4
Step-by-step explanation:
It will terminate after 4 place of decimal
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