Last updated at March 16, 2017 by Teachoo

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Ex1.3, 3 Express the following in the form ๐/๐ where p and q are integers and q โ 0. 0.6 ฬ Let x = 0.6 ฬ = 0.6666โฆ.. Multiplying equation (1) with 10 10x = 10 ร (0.666โฆ) 10x = 6.666โฆ Subtracting (2) from (1) i.e. (2) โ (1) 10x โ x = 6.6666โฆ โ 0. 6666โฆ 9x = 6 x = 6/9 x = 2/3 Thus, 0.6 ฬ = 2/3 Ex1.3, 3 Express the following in the form ๐/๐ where p and q are integers and q โ 0. (ii) 0.47 ฬ Let x = 0.47 ฬ = 0.47777โฆ Multiplying equation (1) with 10 10x = 10 ร (0.47777 โฆ) 10x = 4.7777โฆ Subtracting (2) from (1) i.e. (2) โ (1) 10x โ x = 4.7777โฆ โ 0.47777โฆ 9x = 4.3000 x = 4.3/9 x = 43/90 Thus, 0.47 ฬ = 43/90 Ex1.3, 3 Express the following in the form ๐/๐ where p and q are integers and q โ 0. (iii) 0. (001) ฬ Let x = 0.(001) ฬ = 0.001001โฆ Multiplying equation (1) with 1000 1000x = 1000 ร (0.001001โฆ) 1000x = 1.001001โฆ Subtracting (2) from (1) i.e. (2) โ (1) 1000x โ x = 1.001001โฆ โ 0.001001โฆ 999x = 1 x = 1/999 x = 1/999 Thus, 0.(001) ฬ = 1/999

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.