Question

Question #89bc9

Answer 1

`0.3373737... = 167div495`

Explanation:

If `x=0.3373737...`
then
`color(white)("XXX")1000x=337.37373737...`
`color(white)("XXX")ul(-10x=color(white)("xx")3.37373737...`
`color(white)("XXxx")990x=334`

`rArr x=334/990=167/495color(white)("XX")orcolor(white)("XX")x=167div495`

Answer 2

`x = 167-:495`

Explanation:

let `x = 0.33bar(73)...`

Then multiply by 100 so that only the repeating numbers are to the right of the decimal

`100x = 33.bar(73)..." [1]"`

Multiply by 10000 so that 1 group of the repeating numbers are to the left of the decimal and there are still repeating numbers to the right:

`10000x = 3373.bar(73)..." [2]"`

Subtract equation [1] from [2]:

`10000x - 100x = 3373.bar(73)... - 33.bar(73)...`

`9900x = 3340`

`x = 3340-:9900`

`x = 167-:495`