in this video we'll take a look at several examples of converting angles in radian measure to degree measure to do this conversion we multiply by something called a unit fraction and it's based upon the definition that 2 pi radians is equal to 360° so if we were to take this equation and divide both sides of the equation by 360° as we see here on the left it would simplify to Pi / by 180° is equal to 1 this is a unit fraction but we could also so take the initial equation and divide both sides by 2 pi radians and if we did it would simplify to 1 = 180° divided Pi radians and this is also a unit fraction so we'll use this unit fraction to convert from radians to degrees and we'll use this unit fraction when we convert from degrees to radians so let's take a look at our examples we'll convert this to degrees by multiplying by 180° / Pi radians notice how we're not including the units of radians it's normally assumed that if we have an angle where the units are not degrees it is in radians so now we'll simplify this and then multiply the pi simplifies out 6 and 180 have a common factor of six there's 1 six and six and 30 sixes and 180 and now we'll multiply we have 5 * 30° that's 150° and our denominator would be 1 for our second example we'll do the same again notice how the pi simplifies out 9 and 180 have a common factor of nine so this simplifies to one this simplifies to 20 so we have -2 * 20° that's -40° and again our denominator is equal to 1 now occasionally we'll be given an angle in radians that does not contain a pi but the process is still the same we going to multiply by 180° / Pi notice here nothing simplifies and we normally don't express an angle in degrees with a pi in it so we're going to use the calculator to get a decimal approximation for this angle we're going to have 2.1 time 180 and then we'll divide this by pi so this angle is approximately 12.3 de