Question

The decimal expansion of the rational number 77 560
will terminate after ……….. decimal places (a) 2 (b) 3 (c) 4 (d) 7

Answer 1

Answer:

c. 4

Step-by-step explanation:

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Answer 2

The decimal expansion of the rational number 77/560  will terminate after 4 decimal places

Therefore, option (c) is correct.

Step-by-step explanation:

The given rational number

$=\frac{77}{560}$

$=\frac{77}{7\times 8\times 10}$

$=\frac{11}{2^3\times 10}$

$=\frac{11}{2^3\times 10}\times\frac{5^3}{5^3}$

$=\frac{11\times 5^3}{10\times (2\times5)^3}$

$=\frac{11\times125}{10\times 10^3}$

$=\frac{1375}{10^4}$

$=0.1375$

Therefore, the decimal expansion terminates after 4 decimal places.

Hope this answer is helpful.

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