Question

Express 0.6 +0.¯7 +0.4¯7 in in the form of p/q , where p and q are integers

and q ≠ 0. [ans:299/165]​

Answer 1

Answer:

Step-by-step explanation:

Let x = 0.7Bar

⇒ x = 0.777..........  .........(1)

Multiplying (1) by 10 

⇒ 10x = 7.7...... = 7.777 ...........(2)

Subtracting (1) from (2)

⇒ 10x - x = 9x

 

⇒ 7.777 - 0.777 = 7

   

⇒ 9x = 7 

⇒ x = 7/9

Let y = 0.47Bar

⇒ y = 0.4747 ..............  ........(1)

Multiplying (1) by 100 

⇒ 100y = 47.4747  ............(2)

Subtracting (1) from (2)

⇒ 100y - y = 99y

⇒ 47.4747 - 0.4747 = 47

⇒ 99y = 47

⇒ y = 47/99

Now,

0.7Bar = 7/9

and 0.47Bar = 47/99

0.6 = 6/10

6/10 + 7/9 + 47/99

Taking L.C.M. of the denominator and then solving it, we get.

⇒ (594 + 770 + 470)/990

⇒ 1834/990

⇒ 917/495

Hence, 0.6 + 0.7Bar + 0.47Bar = 917/495

Answer.

Answer 2

Let x=0.7¯=0.777

on multiplying both sides of Eq. (i) by 10, we get

10x=7.77…..

on subtrracting Eq. (i) from Eq. (ii) we get

10x-x= (7.77…)-(0.77….)

9x=7

x=7/9

now let y=0.47¯=0.4777…..

on multiplying both sides of Eq. (ii) by 10, we get

10y= 4.777....

on multiplying both sides . Eq . (iv) by 10, we get

100y= 47.777.....

on subtracting Eq. (iv) from (v), we get

(100y-10y)= (47.777....) - (4.777....)

90y = 43

y= 43/90

0.6+0.7¯+0.47¯=6/10+7/9+43/90

54+70+43/90=167/90