Question

Express each of the following decimals in the form `p/q :` (i)`0. bar(35) ` (ii) `0. bar(585) `

Answer 1

1)`0.overline(35)`
Let `x=0.overline_(35)-(1)`
multiplying by 100
`100x=35.overline(35)-(2)`
`99x=35`
`x=35/99`
2)`0.overline(585)`
Let `x=0.overline(585)-(1)`
multiplying both side by 1000
`1000x=585.overline(585)-(2)`
Subtracting equation 1 from 2
`999x=585`
`x=585/999`.