The number of decimal places after which the decimal expansion of the

1.	The number of decimal places after which the decimal expansion of the rational number \(\frac{23}{2^2\times 5}\) will terminate, isA. 1B. 2C. 3D. 4
Answer» Let x = p/q be a rational number, such that the prime factorization of q is of the form 2ⁿ 5^m, where n, m are non - negative integers. Then x has a decimal expansion which terminates. The maximum power of 2 or 5 in the given rational number is 2. So, it will terminate after 2 places of decimals.

The number of decimal places after which the decimal expansion of the rational number \(\frac{23}{2^2\times 5}\) will terminate, isA. 1B. 2C. 3D. 4

Answer»

Let x = p/q be a rational number, such that the prime factorization of q is of the form 2ⁿ 5^m, where n, m are non - negative integers.

Then x has a decimal expansion which terminates.

The maximum power of 2 or 5 in the given rational number is 2.

So, it will terminate after 2 places of decimals.