Find 5 rational numbers between 4 7 and 5 7 .

Here, we have 4 7 and 5 7 . Let us consider a = 4 7 and b = 5 7 . Rational number between the numbers a and b is a + b 2 . So, the first rational number lies between 4 7 and 5 7 = 4 + 5 14 = 9 14 . Now, consider a = 4 7 and b = 9 14 . So, the rational number lies between them = 4 7 + 9 14 2 = 8 + 9 28 = 17 28 . Now, consider a = 4 7 and b = 17 28 . So, the rational number lies between them = 4 7 + 17 28 2 = 16 + 17 56 = 33 56 . Now, consider a = 9 14 and b = 5 7 . So, the rational number lies between them = 9 14 + 5 7 2 = 9 + 10 28 = 19 28 . Now, consider a = 19 28 and b = 5 7 . So, the rational number lies between them = 19 28 + 5 7 2 = 19 + 20 56 = 39 56 . Thus, the five rational numbers lie between 4 7 and 5 7 are 9 14 , 17 28 , 19 28 , 33 56 , and 39 56 .

Find 3 rational numbers between 2 3 and 3 4 .

We need to find the three rational numbers between 2 3 and 3 4 . Rational number lies between any numbers a and b is a + b 2 . Now, consider a = 2 3 and b = 3 4 So, the first rational number lies between 2 3 and 3 4 = 1 2 2 3 + 3 4 = 1 2 8 + 9 12 = 17 24 . Now, consider a = 2 3 and b = 17 24 . So, the rational number lies between them = 1 2 2 3 + 17 24 = 1 2 16 + 17 24 = 33 48 . Now, consider a = 17 24 and b = 3 4 . So, the rational number lies between them = 1 2 17 24 + 3 4 = 1 2 17 + 18 24 = 35 48 . Thus, the five rational numbers lie between 2 3 and 3 4 are 17 24 , 33 48 and 35 48 .

Express the following decimal number in p q form. 8 . 39 ¯

Let us say, p q = 8 . 39 ¯ ⇒ p q = 8 . 393939 . . . . ( i ) Now, multiply both sides by 100 we get: ⇒ 100 × p q = 100 × 8 . 393939 . . . . ⇒ 100 p q = 839 . 393939 . . . . ( i i ) Subtracting equation ( i ) from equation ( i i ) we get: ⇒ 100 p q - p q = 839 . 393939 . . . . - 8 . 393939 . . . . ⇒ 99 p q = 831 ⇒ p q = 831 99 Hence, the rational number is 831 99 .

Express the following decimal number in p q form. 3 . 12 7 ¯

Let us say, p q = 3 . 12 7 ¯ ⇒ p q = 3 . 127777777 . . . . ( i ) Now, multiply both sides by 100 we get: ⇒ 100 × p q = 100 × 3 . 127777777 . . . . ⇒ 100 p q = 312 . 7777777 . . . . ( i i ) and 1000 p q = 3127 . 777777 . . . . ( i i i ) Subtracting equation ( i i ) from equation ( i i i ) we get: ⇒ 1000 p q - 100 p q = 3127 . 777777 . . . . - 312 . 7777777 . . . . ⇒ 900 p q = 2815 ⇒ p q = 2815 900 = 563 180 Hence, the rational number is 563 180 .

Express the following decimal number in p q form. 5 . 125 ¯

Let us say, p q = 5 . 125 ¯ ⇒ p q = 5 . 125125125 . . . . ( i ) Now, multiply both sides by 1000 we get: ⇒ 1000 × p q = 1000 × 5 . 125125 . . . . ⇒ 1000 p q = 5125 . 125125 . . . . ( i i ) Subtracting equation ( i ) from equation ( i i ) we get: ⇒ 1000 p q - p q = 5125 . 125125 . . . . . . - 5 . 125125 . . . ⇒ 999 p q = 5120 ⇒ p q = 5120 999 Hence, the rational number is 5120 999 .

E M B I B E

Mathematics Class - 9>Algebra>Chapter 2 - Real Numbers (Rational and Irrational Numbers)>Exercise

Chhattisgarh Board Solutions for Exercise 11: Exercise

Author:Chhattisgarh Board

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Exercise 11: Exercise

Attempt the practice questions from Exercise 11: Exercise with hints and solutions to strengthen your understanding. Mathematics Class - 9 solutions are prepared by Experienced Embibe Experts.