Find the smallest positive rational number by which 1/7 should be multiplied so that it's decimal expansion terminates after 2 places of decimals
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Answered by
351
Solution:-
We know that our denominator is in the form of 2^n5^m, then we get terminating decimal digit, and it depends on the value of m or n. If we have m>n, then decimal digit terminates after m or if we have n > m, then digit terminates after n.
And, here we have 1/7. So, our numerator must be 7, so we cancel out 7 from denominator to get terminating decimal digits.
And,
as we know 5 > 2, and 5² > 2². So, to place 5² in denominator we get smaller rational number in comparison to place 2².
Our smallest rational number by which 1/7 should be multiplied, so that its decimal expansion terminates after two places of decimal = 7/5² = 7/25 Answer.
We know that our denominator is in the form of 2^n5^m, then we get terminating decimal digit, and it depends on the value of m or n. If we have m>n, then decimal digit terminates after m or if we have n > m, then digit terminates after n.
And, here we have 1/7. So, our numerator must be 7, so we cancel out 7 from denominator to get terminating decimal digits.
And,
as we know 5 > 2, and 5² > 2². So, to place 5² in denominator we get smaller rational number in comparison to place 2².
Our smallest rational number by which 1/7 should be multiplied, so that its decimal expansion terminates after two places of decimal = 7/5² = 7/25 Answer.
Answered by
196
Sol. We have:1/7
For terminating decimal expansion,7 should be removed from denominator.
Further,for decimal expansions to terminate after 2 decimal places,there should be 2^2×5^5 in denominator.
So, the smallest positive rational number to obtain a decimal expansion terminating after after 2 decimal places is 7/2^2×5^2 = 7/100.
[Note that by multiplying 1/7 by 7/2^2 or 7/5^2 will also give a decimal expansion terminating after two decimal places. But smallest positive rational number is 7/100.]
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