Question

after how many decimal places will the decimal expansion of the rational number 7 raise to 3 by 2 raise to 4 into 5 raise to 3 terminate

Answer 1

23/2^4 x 5^3 = (23x5)/2^4 x 5^4 making the powers of 2 and 5 in the denominator equal, so that we get 115/10^4 = 115/10000= 0.0115.

So, the decimal expansion gets terminated with number of decimal places as much as the power of 10.

Note: A rational number will give a terminating decimal only if the denominator is a product of various powers of 2 and 5.

Otherwise, we get a recurring decimal.