Question

How do you express `7/12` as a decimal representation?

Answer 1

`7/12 = 0.58333... = 0.58bar(3)`

Explanation:

Long divide `7` by `12`...

`color(white)(00000")")underline(color(white)(0)0color(black)(.)5color(white)(0)8color(white)(0)3color(white)(0)3color(white)(.)...)`
`color(white)(00)12color(white)(0)")"color(white)(0)7color(black)(.)0color(white)(0)0color(white)(0)0color(white)(0)0color(white)(.)...`
`color(white)(00000")"0)underline(6color(white)(.)0)`
`color(white)(00000")"0)1color(white)(.)0color(white)(0)0`
`color(white)(00000")"0)underline(color(white)(0)color(white)(.)9color(white)(0)6)`
`color(white)(00000")"00)color(white)(.)color(white)(00)4color(white)(0)0`
`color(white)(00000")"00)color(white)(.)color(white)(00)underline(3color(white)(0)6)`
`color(white)(00000")"00)color(white)(.)color(white)(0000)4color(white)(0)0`
`color(white)(00000")"00)color(white)(.)color(white)(0000)underline(3color(white)(0)6)`
`color(white)(00000")"00)color(white)(.)color(white)(000000)4color(white)(.)...`

Note that the remainder `4` starts repeating, so the quotient does too.

So:

`7/12 = 0.58333... = 0.58bar(3)`