# How do you convert -0.872664626 radians into π terms?

Jul 28, 2015

Use algebra to get $- 0.872664626 \approx - 0.27777777777868 \cdot \pi$ .

#### Explanation:

To write $- 0.872664626$ as a multiple if $\pi$, solve:

$k \pi = - 0.872664626$

So $k = - \frac{0.872664626}{\pi} \approx - 0.277777777778680 . . .$

And $- 0.872664626 \approx - 0.27777777777868 \cdot \pi$

Assuming that you think the answer should be some rational number times $\pi$, you would take this to be

$- 0.2 \overline{7}$. Which is $\frac{5}{18}$. So we would write:

$- 0.872664626 \approx - \frac{5}{18} \pi$