Express 0 . 375 in the form of p q .

Given decimal number is 0 . 375 A decimal number can be expressed in the form of a fraction, keeping all the digits removing the decimal point on the numerator and the denominator is a one followed by a zeroes equals to the number of digits after a decimal point. There are three digits after a decimal point. So, the denominator is the one followed by three zeroes. So, 0 . 375 = 375 1000 The simplified form of the above fraction is 0 . 375 = 375 1000 = 3 8

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.

The decimal expansion of the number 14588 8750 will

Terminate after four decimal place

Terminate after two decimal places

Terminate after three decimal places

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.

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.