Question

The decimal expansion of the rational number $\frac{43}{2^{4}* 5^{3}}$ will terminate after how many places of decimals?

Answer 1

If the factors of denominator of the given rational number is of form 2^m 5ⁿ ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.It terminates after k places of decimals where k is the larger of m and n.

SOLUTION:

Given : 43/2⁴× 5³

43/2⁴× 5³ = 43 × 5¹ /2⁴× 5³ × 5¹

= 215/(2×5)⁴

= 215/ 10⁴

= 215 / 10000  

= 0.0215  

Hence, 43/2⁴× 5³ has terminating decimal expansion. The decimal expansion of  43/2⁴× 5³ terminate after 4 places of decimal.

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Answer 2

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