Question

How do you convert `(5pi)/7` into degrees?

Answer 1

you need to use the conversion `pi=180` to get the answer

Explanation:

`(5*pi)/7` 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:

`(5*pi)/7=x` in the same proportion as `pi=180`

`(5*pi)/7/pi=x/180`

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

`(5*pi)/7*(1/pi)=x/180`

now we simplify the `pi/pi = 1`

`5/7=x/180`

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

`180*(5/7)=x`

`x=900/7=128.571`
(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. :)