Question

How to find the fractional notation for the given infinite sum below? `0.bar17` = `17/100` + `17/10000` + `17/10000000` +.....

Answer 1

`17/99`

Explanation:

`x = 0.171717....`
`=> 100 x = 17.171717...`
`=> 100 x - x = 99 x = 17`
`=> x = 17/99`

Answer 2

`17/99`

Explanation:

`"we reqire to create 2 equations with the repeating decimal"`
`"after the decimal point"`

`0.bar(17)-=0.171717...`

`"let "x=0.bar(17)to(1)`

`"then "100x=17.bar(17)to(2)`

`"subtracting "(2)-(1)" eliminates the repeating decimal"`

`(100x-x)=(17.bar(17)-0.bar(17))`

`99x=17rArrx=17/99`

`rArr0.bar(17)=17/99`