Home
Class 9
MATHS
Express 0.6+0.bar7+0.4bar7 in the form p...

Express `0.6+0.bar7+0.4bar7` in the form `p/q` where p and q are integers and `q ne 0`.

Text Solution

Verified by Experts

Let `x=0.bar7= 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=0.4bar7 =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 `43/90`
`0.6 + 0.bar7+ 0.4bar7=6/10 + 7/9+43/90`
`(54+70+43)/90=167/90`
Promotional Banner

Topper's Solved these Questions

  • NUMBER SYSTEMS

    NCERT EXEMPLAR ENGLISH|Exercise SHORT ANSWER TYPE QUESTIONS|18 Videos

  • LINES AND ANGLES

    NCERT EXEMPLAR ENGLISH|Exercise MULTIPLE CHOICE QUESTIONS|34 Videos

  • POLYNOMIALS

    NCERT EXEMPLAR ENGLISH|Exercise EXERCISE 2.4 Long Answer type Questions|9 Videos

Similar Questions

Explore conceptually related problems

Express 0. 99999 in the form p/q , where p and q are integers and q!=0.

Express the following in the form p/q , , where p and q are integers and q!=0 .(i) 0. bar6 (ii) 0. bar 47 (iii) 0. bar 001

Show that 0. 3333. . . .=0. bar3 can be expressed in the form p/q , where p and q are integers and q!=0 .

Show that 1. 272727. . .=1. bar 27 can be expressed in the form p/q , where p and q are integers and q!=0 .

The value of 1.999 ….. In the form of p/q , where p and q are integers and q ne 0 , is

Show that 0. 2353535. . .=0. 2 bar 35 can be expressed in the form p/q , where p and q are integers and q!=0 .

Show that 0. 2353535. . .=0. 2 bar 35 can be expressed in the form p/q , where p and q are integers and q!=0 .

Show that 1. 272727=1. bar27 can be expressed in the form p/q , where p\ a n d\ q are integers and q!=0.

Is zero a rational number? Can it be written in the form p/q , where p and q are integers and q ne 0 ?

Show that 3.142678 is a rational number. In other words, express 3.142678 in the form p/q , where p and q arc integers and q!=0 .