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

Aug 3, 2015

you need to use the conversion $\pi = 180$ to get the answer

#### Explanation:

$\frac{5 \cdot \pi}{7}$ 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:

$\frac{5 \cdot \pi}{7} = x$ in the same proportion as $\pi = 180$

$\frac{5 \cdot \pi}{7} / \pi = \frac{x}{180}$

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

$\frac{5 \cdot \pi}{7} \cdot \left(\frac{1}{\pi}\right) = \frac{x}{180}$

now we simplify the $\frac{\pi}{\pi} = 1$

$\frac{5}{7} = \frac{x}{180}$

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

$180 \cdot \left(\frac{5}{7}\right) = x$

$x = \frac{900}{7} = 128.571$
(we changed the direction at the end to follow convention)

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. :)