Question

How do you convert 8/17 into a percent and decimal?

Answer 1

Decimal representation is a periodic decimal fraction:

`8/17 = 0.47058823529411764705882352941176...`
with period `4705882352941176`

As an approximate percentage,

`8/17 ~~ 47.06%`

Explanation:

First of all, you have to convert it into decimal by actually dividing `8` by `17` (in this case the result is periodic decimal fraction, so we can do it only approximately):

`8/17 = 0.47058823529411764705882352941176...`

As you see, `4705882352941176` is a period that is repeated infinite number of times.
So, you may express it using [...] to signify a period as
`8/17 = 0.[4705882352941176]`

Next, you have to decide about precision since it's not practical to carry too many digits. Assume, you decide that for your calculations it is sufficient to have a precision of `0.0001`. Then you round the above number to `0.4706`. Notice that the fourth digit after a decimal point `5` is rounded up to `6` because the following digit is `8`.

Lastly, to convert a decimal fraction into percentage, you just multiply it by `100`, effectively shifting the decimal point two places to the right:
`0.4706 = 47.06%`.