Converting Between Decimal Degrees and Degrees, Minutes, and Seconds

0:00 - Intro
1:31 - Definition of DMS
2:27 - Process for DMS to Decimal
3:10 - Process for Decimal to DMS
4:11 - Example Decimal to DMS
5:50 - Example DMS to Decimal
7:59 - Closing

This is the sixth video in a series made for high school and college math students. This series focuses on basic trigonometry skills necessary for math success.

Today we're going to be talking about two ways of representing fractions of a degree - decimal degrees and degrees - minutes - and seconds.

One degree is equal to 1, 360th of a circle and is notated by an open circle. So, to notate 47 degrees we write this.

But, sometimes we need more precision. To represent fractions of a degree we can either use decimal degrees, or we can use DMS notation.

Decimal degrees are notated similarly to whole degrees, they just have extra digit places after the decimal place. For example, here is a picture of an angle. The measure of this angle is 47 and 36 hundredths degrees. In decimal degrees it is written like this, 47.36 degrees.

DMS stands for Degrees - Minutes - and Seconds.

In DMS notation, 1 degree can be subdivided into 60 minutes. These minutes are represented by a single quotation mark. So 47 degrees - 21 minutes is written like this.

Furthermore, 1 minute can be subdivided into 60 seconds. These seconds are represented by a double quotation mark. So, 47 degrees - 21 minutes - and 36 seconds is written like this.

It so happens that 47 point 36 degrees is the same measure as 47 degrees - 21 minutes - and 36 seconds. How do I know they are the same? Well, one way I can check is to convert from Degrees - Minutes - and Seconds to Decimal degrees. To do that, divide the minutes by 60 and the seconds by 3600.

47 degrees 21 minutes and 36 seconds is equal to
47 plus 21/60 plus 36/3600 which is equal to
47 plus 0.35 + 0.01 which is equal to

47.36 degrees

Another way you you can verify that these are equivalent is to convert from Decimal degrees to degrees - minutes and seconds. To do that, multiply the decimal portion of the degree by 60 to obtain your minutes. Then multiply the decimal portion of the minutes to get your seconds.

To find the minutes for 47.36 degrees we multiply the decimal portion of the degree, .36, by 60. .36 times 60 is 21.6. So 47.36 degrees is the same as 47 degrees and 21.6 minutes.

Now to find the seconds for 47 degrees and 21.6 minutes, we multiply the decimal portion of the minutes, .6, by 60. .6 times 60 is 36. So 47.36 degrees is the same as 47 degrees, 21 minutes, and 36 seconds.

Let's see how this works with a couple of examples.

First we will work on converting from decimal degrees to degrees minutes and seconds. On Catalina Island, off the Southern California coast, there is beach and campsite that you can only reach by sea, Long Point. Suppose we'd like to visit long point. We are given the GPS coordinates of 33.42 degrees north and 118.38 degrees west. But our GPS device wants DMS notation instead. No problem, a little arithmetic will solve that problem.

First, let's convert 33.42 degrees north to DMS.

That's 33 degrees and .42 times 60 minutes = 33 degrees 25.2 minutes,
= 33 degrees, 25 minutes, and .2(60) seconds. Or
33 degrees, 25 minutes and 12 seconds North.

Now, let's convert 118.38 degrees west to DMS.
That's 118 degrees and .38(60) minutes or
= 118 degrees and 22.8 minutes,
= 118 degrees, 22 minutes, and .8(60) seconds or
118 degrees, 22 minutes, and 48 seconds West.

So Long Point can be found at 33 degrees, 25 minutes and 12 seconds North, 118 degrees, 22 minutes, and 48 seconds West.

Now Let's practice converting from degrees, minutes, and seconds to decimal degrees.

I've been wanting to visit the Georgia Aquarium for a long time. They have the only aquarium with I know about with Whale Sharks, wow. I have the latitude and longitude coordinates for the Atlanta Aquarium. They are 33 degrees 45 minutes and 26.99 seconds north and negative 84 degrees 23 minutes and 22.79 seconds west. But now my GPS device needs decimal degrees. What are we going to do?

We can use our knowledge of trigonometry to solve this problem.

First, let's convert 33 degrees 45 minutes 26.99 seconds north to decimal degrees. Remember, we need to divide the minutes by 60 and the seconds by 3600.

This is 33 + 45/60 + 26.99/3600 or approximately
33.757497 degrees north.

Now let's convert negative 84 degrees 23 minutes and 22.79 seconds west to decimal degrees.

This is negative 84 + 23/60 + 22.79/3600 or approximately
- 84.383333 degrees west

So the Georgia Aquarium is at approximately 33.76 degrees north and negative 84.38 degrees west.

[mathquarium]

0:00 - Intro
1:31 - Definition of DMS
2:27 - Process for DMS to Decimal
3:10 - Process for Decimal to DMS
4:11 - Example Decimal to DMS
5:50 - Example DMS to Decimal
7:59 - Closing

[heidishelton]

Awesome video! This made so much sense!