Question

Find the smallest positive rational number by which 1/7 should be multiplied so that its decimal expansion terminates after 2 places of decimal

Answer 1

Step-by-step explanation:

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 .