Question

1. Express 0.777… in the form of p/q, where p and q are integers and q≠0.
2. Express 2.989898…. in the form of p/q, where p and q are integers and q≠0.
3. Do the exercise 1.3 in pg no;12 (Qn no;3 GR9 Ncert).
4. Express 5.3252525… in the form of p/q, where p and q are integers and q≠0.
5. Visualize the following on the number line, using successive magnification
i) 5.726
ii)3.7878…

Answer 1

Given :   0.777…..... =    0. $\overline{7}$

to find : express in form of p/q

Solution:

Let say N = 0.77777777......

=> N =     $0.\overline{7}$

  10N  =   7.7777777.......

=> 10N  =   7. $\overline{7}$

10N - N =  7. $\overline{7}$ - $0.\overline{7}$

=> 9N = 7

=> N = 7/9

=> 0.777…  =  $0.\overline{7}$   = 7/9

A = 2.989898....

100A  = 298.989898....

=> 99A = 296

=> A = 296/99

=> 2.989898....  = 296/99

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Answer 2

Given :   0.777….....   

To find: express in form of p/q

Solution:

Let say n = 0.77777777......

n= $0.\bar{7}$

since the bar is on one digit only multiply the equation by 10 we get

10n  =   7.7777777.......

10n  =   $7.\bar{7}$

10n - n =  7.  - $0.\bar{7}$

9n = 7

n = $\frac{7}{9}$

hence , $0.77777...=\frac{7}{9}$