Express the following decimal number in p q form. 16 . 8

A rational number can be represented in p q form where q ≠ 0 . Given, 16 . 8 It is terminating decimal number. There are one place after decimal point so the numerator will be 10 and we will remove the decimal point. Thus, the rational number form of 16 . 8 = 168 10 Hence, p = 168 , q = 10 , p q = 168 10 .

Express the following decimal number in p q form. 105 . 25

A rational number can be represented in p q form where q ≠ 0 . Given, 105 . 25 It is terminating decimal number. There are two places after decimal point so the numerator will be 100 and we will remove the decimal point. Thus, the rational number form of 105 . 25 = 10525 100 Hence, p = 10525 , q = 100 , p q = 10525 100 .

Express the following decimal number in p q form. 7 . 36

A rational number can be represented in p q form where q ≠ 0 . Given, 7 . 36 It is terminating decimal number. There are two places after decimal point so the numerator will be 100 and we will remove the decimal point. Thus, the rational number form of 7 . 36 = 736 100 Hence, p = 736 , q = 100 , p q = 736 100 .

Express the following decimal number in p q form. 0 . 70 ¯

Let us say, p q = 0 . 70 ¯ ⇒ p q = 0 . 707070 . . . . ( i ) Now, multiply both sides by 100 we get: ⇒ 100 × p q = 100 × 0 . 707070 . . . . ⇒ 100 p q = 70 . 707070 . . . . ( i i ) Subtracting equation ( i ) from equation ( i i ) we get: ⇒ 100 p q - p q = 70 . 707070 . . . . - 0 . 70707070 . . . . ⇒ 99 p q = 70 ⇒ p q = 70 99 Hence, the rational number is 70 99 .