Question

How do you write `300/1800` as a percentage?

Answer 1

`16 2/3%` as an exact value

A lot of detail given so you can see where everything comes from.

Explanation:

`color(blue)("Something to think about")`

Percentage is basically a fraction. However, it is a special fraction in that the bottom number (denominator) is fixed at 100

Suppose for example we have 20 percent. This can be written as

`20/100" or "20%` they are both the same thing

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

The whole (all of it) is the count of `1800`

The part of the whole is the count of `300`

So expressing this as a fraction of the whole we have: `300/1800`

But this needs to be expressed as a percentage so we have:

`300/1800=("some count")/100`

Let the unknown count (value) be represented by `x` giving:

`300/1800=x/100`

We need to get `x` on its own on one side of the = and everything else on the other side. Thus we need to 'get rid' of the `100" from "x/100`

Multiply both sides by 100

`color(green)(300/1800=x/100 color(white)("dddd") ->color(white)("dddd") 300/1800color(red)(xx100)=x/100color(red)(xx100)`

`color(green)(color(white)("dddddddddddddd") ->color(white)("dddd") 300/cancel(1800)^18color(red)(xxcancel(100)^1)=x/cancel(100)^1color(red)(xxcancel(100)^1)`

`color(green)( color(white)("dddddddddddddd") ->color(white)("ddddddddd") 16 12/18color(white)("dd.d)=x )`

But `12/18->(12-:6)/(18-:6)=2/3 color(green)(->color(white)("ddddd")16 2/3 color(white)("dddd")=x)`

As `1/3=0.33333...` where the 3's go on for ever
then `2/3=0.6666...` where the 6's go on for ever

So we have three options for the answer format

`color(red)("EXACT FRACTION VALUE "-> color(white)("ddddd") x=16 2/3%)`

`color(red)("EXACT DECIMAL ANSWER "-> color(white)("ddddd") x~~16.66bar6%`

Note that the bar over the last 6 means it goes on for ever

Or you can round the decimal which is not exact

`color(red)("APPROXIMATE DECIMAL ANSWER "-> color(white)("dd") x~~16.667`
Rounded to 3 decimal places

Answer 2

See a solution process below:

Explanation:

"Percent" or "%" means "out of 100" or "per 100", Therefore x% can be written as `x/100`.

So we can write and solve for `x`:

`x/100 = 300/1800`

`x/100 = (color(blue)(cancel(color(black)(3)))1color(red)(cancel(color(black)(00))))/(color(blue)(cancel(color(black)(18)))6color(red)(cancel(color(black)(00))))`

`x/100 = 1/6`

`color(red)(100) xx x/100 = color(red)(100) xx 1/6`

`cancel(color(red)(100)) xx x/color(red)(cancel(color(black)(100))) = 100/6`

`x = 16.6666666666666...`

Or

`x = 16.7` rounded to the nearest tenth#

Or

`x = 16.bar6`

Therefore:

`(16.bar6)/100 = 16.bar6%`