Question

6. Express 0.6 + bar 0.7 + bar 0.47 in the form p/q, where p and q are integers and q not equal to zero​

Answer 1

0.6=6/10

bar 0.7 =

x=0.7777....

multiply 10 by both the sides

x×10=0.777...×10

10x=7.777...

subtract the above two equations

10x-x=7.777...-0.777...

9x=7

x=7/9

bar 0.47 =

x=0.4747....

multiply 100 by both the sides

x×100=0.4747...×100

100x=47.4747....

subtract the above two equations

100x-x=47.4747...-0.4747...

99x=47

x=47/99

now,

6/10+7/9+47/99

LCM of 10,9,99 = 990

6×99/10×99=594/990

7×110/9×110=770/990

47×10/99×10=470/990

hence, 594/990+770/990+470/990=

1834/990

=917/495