Question

What is the decimal equivalent of 5/12?

Answer 1

`5/12=0.41666....=0.41bar6`

Explanation:

Please refer to [a similar question for details.](https://socratic.org/questions/how-do-you-write-12-8-as-a-decimal#341159)

As `5/12` is already in smallest form and factors of denominators are `2xx2xx3`. As prime factors are other than `2` and `5`, we have to long divide `5` by `12` and answer will have repeating numbers after decimal point.

`color(white)(xxxxxx)0.4 color(white)(x)1color(white)(x)6color(white)(x)6`
`color(white)(xx) 12| bar(5color(white)(x).0color(white)(x) 0)color(white)(x) 0`
`color(white)(xxxxx)ul(4color(white)("x)8)color(red)(darr`
`color(white)(xxxxxxx)2 color(white)(x) "0"`
`color(white)(xxxxxxx)ul(1 color(white)(x) 2 )"`
`color(white)(xxxxxxxxx) 8 color(white)(x) "0"`
`color(white)(xxxxxxxxx)ul(7 color(white)(x) 2 )"`
`color(white)(xxxxxxxxxxx) 8 color(white)(x) "0"`
`color(white)(xxxxxxxxxxx)ul(7 color(white)(x) 2 )"`
`color(white)(xxxxxxxxxxxxx) 8`

As the remainder continues to be `8`, the digit `8` will repeat endlessly and hence

`5/12=0.41666666666..` or `0.41bar6`