Question

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

Answer 1

let `x=1.27272727..........`
multiplying it by 100 we get
`100x = 127.272727......`
`127.272727..... = 126 + 1.272727.......`
`100x = 126 + x`
`99x = 126`
`x=126/99`
`x= 14/11`
answer