Question

How do you convert `(8pi)/3` into degrees?

Answer 1

we need to use `pi=180` to convert

Explanation:

`(8*pi)/3` is a radian measure which needs to be converted to degrees. For that we need a simple conversion factor: `pi=180`

Now we are going to setup an equation with the conversion factor. A nice way to do this is to take advantage of the proportionality of the problem. So we set the equations up like this:

`(8*pi)/3=x` in the same proportion as `pi=180`

`(8*pi)/3/pi=x/180`

we want to simplify this by changing the division to a multiplication

`(8*pi)/3*(1/pi)=x/180`

now we simplify the `pi/pi = 1`

`8/3=x/180`

to solve we simply undo the division on x with a multiply

`180*(8/3)=x`

`x=480`
(we changed the direction at the end to follow convention)

NOTE: always put the same units in the same fraction
`(rad)/(rad)=(degrees)/(degrees)`

and that makes us happy. :)