Question

express 0.6 +0.bar 7 +0.4bar 7 in the form of p/q​

Answer 1

Answer:

1837/990 is your answer

Step-by-step explanation:

0.6+0. bar 7+0.4 bar 7

0.6=6/10

now we have to convert 0.bar 7 and 0.4bar 7 in the form of p/q

let x =0.bar 7____(1)

10x=7.bar 7 multiply by 10 on both sides

10x=7+x____(1)

9x=7 x=7/9

now taking 0.4bar 7

let y=0.4bar 7____(2)

100y=47.bar 77 multiply by 100 on both sides

100y=47.30+0.4bar 7

100y=47.30+y____(2)

99y=47.30

y=47.30/99

now we got all in p/q form ie. 6/10 +7/9 +47.30/99

adding them

(99×6+7×110+10×47.30)/990

594+770+473÷990

1837/990

hope it helps you thanks

Answer 2

Answer:

 167/90

Solution:-

0.6 + 0.bar 7 + 0.4 bar 7

-----

0.6 = 6/10

-----

Let x be 0.777...  

    x = 0.777... --- [1]

=>  10x = 10 * 0.777... (Multiply both side with 10)

=>  10x = 7.77....   --- [2]

=>  10x - x = 7.77... - 0.777...  ( Subtract [1] from [2] )  

=>  9x = 7  

    x = 7/9

------

 

 Let y be 0.4777

     y = 0.4777... -- [1]

=> 10x = 4.777....  --[2] (Multiply with both side with 10)

=> 10x * 10 = 10 * 4.77... -- [3] (Multiply both side with another 10)  

=> 100x = 47.77...

=> 100x - 10x = 47.77.. - 4.77... (Subtract [2] from [3])

=> 90x = 43  

    x = 43/90

------

Now,

  6/10 + 7/9 + 43/90

LCM of 10, 9 and 90 = 90 (2, 3, 5 ,5)

 6*9 + 7*10 + 43*1            (6*9 + 7*10 + 43*1/90)

-------------------                  

        90

   54 + 70 + 43

------------------

        90

=   167

  -----   == 167/90

   90