Question

The decimal expansion of the rational number \[\frac{14587}{1250}\]  will terminate after

Options

• one decimal place

• two decimal place

• three decimal place

• four decimal place

Answer 1

We have,

`14587/1250=14587/(2^1xx5^4)`

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  4   places of decimal.

Hence, the correct choice is (d).