Question

The number of decimal place after which the decimal expansion of the rational number \[\frac{23}{2^2 \times 5}\] will terminate, is

Options

• 1

• 2

• 3

• 4

Answer 1

We have,

`23/(2^2xx5^1)`

Theorem states: 

Let `x= p/q` be a rational number, such that the prime factorization of q is of the form `2^mxx5^n`, where m andn are non-negative integers.

Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of mand n.

This is given that the prime factorization of the denominator is of the form`2^mxx5^n`.

Hence, it has terminating decimal expansion which terminates after 2 places of decimal.

Hence, the correct choice is (b).