Question

find the smallest positive natural number bye which1/7should be multiplied so that it's decimal expansion terminates after 2 places of decimal.
explain with ful solution​

Answer 1

Answer:

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.]