Question

How do you find the fraction notation and simplify 16.6%?

Answer 1

`16.6%=83/500`, this is roughly equal to `1/6`.

Explanation:

`x%` can be written in fraction notation as `x/100`

Hence `16.6%=16.6/100=166/1000=83/500`

This is roughly equal to `1/6` as

`1/6=(83.33333333....)/500=16.666666.....%`

Answer 2

`16.667 = 16 2/3% = (16 2/3)/100 = (50/3)/100 = 50/300 = 1/6`

Explanation:

I am making an assumption that this is meant to be `16.dot6`, rather than 16.6 as given.

The percentage in this case would usually be given in a more accurate form of #16.7% or 16.67%, implying that it is a recurring decimal which has been rounded off.

The best way of giving it is `16 2/3%` which is accurate.

This is one of the common percentages which is useful to know by heart.
`16 2/3% = (16 2/3)/100 = (50/3)/100 = 50/300 = 1/6`

The other fractions in this family are:

`2/6 = 1/3 = 33 1/3% = 0.333`

`3/6 = 1/2 = 50% = 0.5`

`4/6 = 2/3 = 66 2/3% = 0.667`

`5/6 = 83 1/3% = 0.833`

Other common fractions are
`1/4 = 25% = 0.25`
`3/4 = 75% = 0.75`

Answer 3

`83/500`

Explanation:

There are two ways of writing percentages. In sentences etc you would write 16.6% but for calculation you would write `16.6/100`

Not that `16.6/100` is the same as `16.6-:100`

To get rid of the decimal point multiply both top (numerator) and bottom (denominator) by 10:

`(16.6xx10)/(100xx10)= 166/1000`

Both numerator and denominator are even so divide both by 2

`(166-:2)/(1000-:2) = 83/500`