Question

0.407(bar7) solution

Answer 1

x=0.407777..
100x=40.777 (1
1000x=407.77... (2

subtaract 1 from 2

1000x-100x=407.77-40.77
900x=367
x=367/900

Answer 2

let

X=0.407777777... equation 1

periodicity 1

so multiply with 10

10( X=0.407777...)

10x= 04.07777......equation 2

10x=04.077777
-. x= 0.407777
_____________
9x= 03 . 6700
_____________

9x=3.67

X= 3.67/9

X=367/900