Welcome back mathematicians. In this video we are going to convert angles between degrees and degrees minutes and seconds. So one minute which is equal to 1 60th of a degree is represented as one with a single tick mark.
Then one second is equal to 1 60th of a minute which is equal to 1 over 3600th of a degree. So we represent one second with one followed by the double tick marks. Typically, you will see degrees, minutes, and seconds paraphrased as capital D with the degree symbol, followed by capital M with the minute symbol, followed by capital S with the second symbol.
In our first problem, we're going to convert this angle to a decimal in degrees. Right now, we have degrees, minutes, and seconds. We're going to round our answer to two decimal places.
So we're going to start by rewriting this as 40 degrees plus 10 minutes. plus 25 seconds. And our goal is to convert the minutes and seconds over two degrees and then add them all up for a final answer. 40 degrees, there's nothing really to do with that because it's already in the unit that we want.
But we do need to convert 10 minutes. So we're going to multiply 10 minutes times 1 60th of a degree because each minute is worth 1 60th of a degree. We're then going to add 25 seconds times 1 over 3600th of a degree because again one second is equal to that 1 over 3600th of a degree.
We then find the product and so we have 40 degrees plus 10 times 1 over 60 and then reduce it you get 1 6th of a degree and then you take 25 times 1 over 3600. and reduce, and what you end up getting is 1 over 144 of a degree. And then we add them all up, and what we end up getting is 40 and 25 over 144. But we do want an answer in decimal form, rounded to two decimal places. So take 25 divided by 144, I did forget my degree symbol, and then combine that with 40, or add that to 40. and what you end up getting is 40.17 again rounded to two decimal places.
So that's how you convert from degrees, minutes, seconds, over to degrees in decimal form, rounded to whatever decimal place you're directed to do. Now we're going to convert this angle in degrees to degrees, minutes, and seconds form. So to do this we're actually going to break up the 61.24 degrees as 61 degrees plus 0.24 degrees.
We are then going to multiply to convert the 0.24 degrees over into minutes. We're going to do the reciprocal of what we did in the previous problem. Instead of multiplying by 1 over 60, we're going to multiply by 60. And so what we end up getting is 61 degrees plus 14.4 minutes.
Now we need to convert the 0.4 minutes over into seconds. So this is going to be 61 degrees plus 14 minutes plus 0.4 minutes times and now you're not going to multiply by 3600 because that would be if we were converting the degrees into seconds we're converting minutes to seconds so what we're actually going to multiply by is 60. so when we do that we get 61 degrees plus 14 minutes plus 24 seconds and so to rewrite this in terms of degrees minutes and seconds it's 61 degrees 14 minutes and 24 seconds all right guys good luck