Question

express 0.6 + 0.7bar + 0.47(here bar is on seven) in the form p/q, p and q are integers

Answer 1

let x=0.47777777........ so 10x=4.77777.....
10x-x=4.3
x=43/90

let y =0.777777 ............  so 10y=7.77777.......
10y-y=7
y=7/9

required sum = (6/10)+(43/90)+(7/9)
=167/90

Answer 2

167/90

Step-by-step explanation:

Let x be 0.777...(i)

If we multiply it by 10, we get;

10x = 7.777...(ii)

by subtracting (i) from (ii),

⇒ 10x - x = 9

⇒ 7.777... - 0.777... = 7

⇒ 9x = 7

∵ x = 7/9

Similarly, let x be 0.4777...(i)

By multiplying (i) by 10, we get;

10y = 4.7777...(ii)

Now, subtracting (i) from (ii),

⇒ 10y - y = 9y

⇒ 4.7777... - 0.4777... = 4.3

⇒ 9y = 4.3

∵ y = 43/90

So,

0.6 + 7/9 + 43/90

= 6/10 + 7/9 + 43/90

= (54 + 70 + 43)/90

= 167/90

Thus, 167/90 is the answer.

Learn more: Write in p/q form

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