Question

How do you convert 1/3 into a decimal and percent?

Answer 1

`1/3` as a decimal `->0.3bar3`

`1/3` as a percentage `->(33.3bar(3))/100 -> 33.3bar(3)%`

Explanation:

`color(blue)("Determining the decimal value of "1/3)`

If you apply long division you soon observe a repeating pattern. You would have demonstrated that this pattern goes on forever. The number is:

`0.3333333333333.....`

The mathematical way to show the repeating process is to put a bar over the last 3 that you write. So you would get:

`0.3bar3`
.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determining the percentage equivalent of "1/3)`

The first decimal place is `1/10color(white)()^("ths")`

The second decimal place is `1/100color(white)()^("ths")`

As percentage is really `1/100color(white)()^("ths")` then we would write:

`(33.3bar(3))/100 -> 33.3bar(3)%`