Without actually performing long division method, state whether 17 6 will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Given, 17 6 We know that, If the denominator of a rational number is of the form 2 m × 5 n , then the rational number can be expressed as a terminating decimal. Else, it can be non-terminating decimal. Here, we need to split 6 into its prime factors. ⇒ 6 = 2 × 3 Here, the denominator is not of the form 2 m × 5 n . Hence, 17 6 has a non-terminating recurring decimal expansion.

Without actually performing long division method, state whether 17 6 will have a terminating decimal expansion or a non-terminating recurring decimal expansion.

Given, 17 6 We know that, If the denominator of a rational number is of the form 2 m × 5 n , then the rational number can be expressed as a terminating decimal. Else, it can be non-terminating decimal. Here, we need to split 6 into its prime factors. ⇒ 6 = 2 × 3 Here, the denominator is not of the form 2 m × 5 n . Hence, 17 6 has a non-terminating recurring decimal expansion.

Without actually performing the long division, state whether the rational number 35 50 will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Given rational number is 35 50 . Prime factorising the denominator 50 , 50 = 2 × 5 × 5 = 2 1 × 5 2 Since the factors of the denominator are in the form 2 m and 5 n , the given rational number will have a terminating decimal expansion.

State whether the decimal expansion of a rational number 7 80 is terminating or non terminating recurring. Without performing the long division method.

Given number is 7 80 Let x = p q be a rational number, such that the prime factorisation of q is of the form 2 n 5 m , where n , m are non-negative integers. Then, x has a decimal expansion which terminates. Now, 80 = 2 4 × 5 Here denominator is of the form 2 n 5 m . Therefore, 7 80 is terminating.

The decimal expansion of the number 14588 8750 will

Terminate after four decimal place

Terminate after two decimal places

Terminate after three decimal places

Find a rational number between 2 and 3 .

We know the decimal form of 2 and 3 as: 2 = 1 . 4142135 . . . . . 3 = 1 . 73205080 . . . . . . As we know that rational numbers are those decimal numbers which are either terminating or repeating. So, you can given any terminating or repeating decimal number between 1 . 4142135 . . . and 1 . 73205080 . . . as your answer. So, numbers between 2 and 3 are just greater than 1 . 41 and less than 1 . 73 . Thus answer can be any of the following rationals: 1 . 415 , 1 . 416 , 1 . 417 , 1 . 532 , 1 . 582 , 1 . 60 , 1 . 62 , 1 . 70 , 1 . 72 etc.