# How do you convert -3.5 to degrees?

Aug 3, 2015

use the conversion $\pi = 180$

#### Explanation:

-3.5 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:

$- 3.5 = x$ in the same proportion as $\pi = 180$

$- \frac{3.5}{\pi} = \frac{x}{180}$

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

$180 \cdot - \frac{3.5}{\pi} = x$

$- \frac{630}{\pi} = x$
now it is a matter of how many decimals. Let us say that we are using the standard 3.14 approximation and need two decimal places.

$- \frac{630}{3.14} = x$
$x = - 200.64$
(we changed the direction at the end to follow convention)

this should make sense because 3.5 is a little bigger than 3.14 and 200 is a little bigger than 180. And don't forget the sign!

NOTE: always put the same units in the same fraction
$\frac{r a d}{r a d} = \frac{\mathrm{de} g r e e s}{\mathrm{de} g r e e s}$

and that makes us happy. :)