Convert the following decimal numbers in the form of p q ( p , q ∈ Z and q ≠ 0 ) . 0 . 3 ¯

Let x = 0 . 3 ¯ = 0 . 3333 . . . . . 1 (Here period of decimal is 1 , multiply equation 1 by 10 ) 10 x = 3 . 3333 . . . . . 2 Subtract the first equation from second, we get 10 x - x = 3 . 33 - 0 . 33 9 x = 3 or x = 1 3 Hence, the required value is 1 3

Convert the following decimal numbers in the form of p q ( p , q ∈ Z and q ≠ 0 ) . 2 . 124 ¯

Let x = 2 . 124 ¯ = 2 . 124124124 . . . . 1 (Here period of decimal is 3 , multiply equation 1 by 1000 .) 1000 x = 2124 . 124124124 . . . . . . 2 Subtract the first equation from second, we get 1000 x - x = 2124 . 1241 - 2 . 1241 999 x = 2122 x = 2122 999 Hence, required answer is 2122 999

Convert the following decimal numbers in the form of p q ( p , q ∈ Z and q ≠ 0 ) . 0 . 4 5 ¯

Let x = 0 . 4 5 ¯ = 0 . 45555 . . . . . 1 (Here the repeating decimal digit is 5 , which is the second digit after the decimal point, multiply equation 1 by 10 ) 10 x = 4 . 5555 . . . . . 2 (Now period of decimal is 1 , multiply equation 2 by 10 ) 100 x = 45 . 5555 . . . . . . 3 Subtract second equation from third, we get 100 x - 10 x = 45 . 5555 - 4 . 5555 90 x = 41 x = 41 90 Hence, required answer is 41 90

Convert the following decimal numbers in the form of p q ( p , q ∈ Z and q ≠ 0 ) . 0 . 5 68 ¯

Let x = 0 . 5 68 ¯ = 0 . 5686868 . . . . . 1 (Here the repeating decimal digit is 68 , which is the second digit after the decimal point, so multiply equation 1 by 10 ) 10 x = 5 . 686868 . . . . . . 2 (Now period of decimal is 2 , multiply equation 2 by 100 ) 1000 x = 568 . 686868 . . . . . 3 Subtract second equation from third, we get 1000 x - 10 x = 568 . 6868 - 5 . 6868 990 x = 563 x = 563 990 Hence, required answer is 563 990 .

E M B I B E

Mathematics Standard 9>Chapter 2 - Real Numbers>Exercise

Tamil Nadu Board Solutions for Chapter: Real Numbers, Exercise 6: Exercise

Author:Tamil Nadu Board

Tamil Nadu Board Mathematics Solutions for Exercise - Tamil Nadu Board Solutions for Chapter: Real Numbers, Exercise 6: Exercise

Attempt the free practice questions on Chapter 2: Real Numbers, Exercise 6: Exercise with hints and solutions to strengthen your understanding. Mathematics Standard 9 solutions are prepared by Experienced Embibe Experts.