Ex 1.3,3 - Express the following in form p/q - (i) 0.6 - Expressing decimal in p/q

 

  1. Chapter 1 Class 9 Number Systems
  2. Serial order wise
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Ex1.3, 3 Express the following in the form ๐‘/๐‘ž where p and q are integers and q โ‰  0. 0.6 ฬ… Let x = 0.6 ฬ… = 0.6666โ€ฆ.. Multiplying equation (1) with 10 10x = 10 ร— (0.666โ€ฆ) 10x = 6.666โ€ฆ Subtracting (2) from (1) i.e. (2) โ€“ (1) 10x โ€“ x = 6.6666โ€ฆ โ€“ 0. 6666โ€ฆ 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‘ž where p and q are integers and q โ‰  0. (ii) 0.47 ฬ… Let x = 0.47 ฬ… = 0.47777โ€ฆ Multiplying equation (1) with 10 10x = 10 ร— (0.47777 โ€ฆ) 10x = 4.7777โ€ฆ Subtracting (2) from (1) i.e. (2) โ€“ (1) 10x โ€“ x = 4.7777โ€ฆ โ€“ 0.47777โ€ฆ 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‘ƒ/๐‘ž where p and q are integers and q โ‰  0. (iii) 0. (001) ฬ… Let x = 0.(001) ฬ… = 0.001001โ€ฆ Multiplying equation (1) with 1000 1000x = 1000 ร— (0.001001โ€ฆ) 1000x = 1.001001โ€ฆ Subtracting (2) from (1) i.e. (2) โ€“ (1) 1000x โ€“ x = 1.001001โ€ฆ โ€“ 0.001001โ€ฆ 999x = 1 x = 1/999 x = 1/999 Thus, 0.(001) ฬ… = 1/999

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