College Algebra & Trigonometry, 2018a

8.1. MEASURING ANGLES 345
Examples
Convert 21.85 ◦ to DMS units
0.85 ∗ 60 = 51
So, 21.85 ◦ =21 ◦ 51 ′
Convert 143.27 ◦ to DMS units
0.27 ∗ 60 = 16.2
So, 143.27 ◦ = 143 ◦ 16.2 ′
In order to compute the number of seconds needed to express this angle in DMS
units, we take the decimal portion of the minutes and multiply by 60:
0.2 ∗ 60 = 12
So, 143.27 ◦ = 143 ◦ 16.2 ′ = 143 ◦ 16 ′ 12 ′′
In the example above we ended with a whole number of seconds. If you don’t get
a whole number for the seconds then you can leave the seconds with a decimal
portion. For example, if you wanted to convert 22.847 ◦ to DMS units:
22.847 ◦ =22 ◦ 50.82 ′ =22 ◦ 50 ′ 49.2 ′′
Converting from DMS to decimal
To convert from DMS units to decimals, simply take the seconds portion and
divide by 60 to make it a decimal:
129 ◦ 19 ′ 30 ′′ = 129 ◦ 19.5 ′
Then take the new minutes portion and divide it by 60
19.5
60 =0.325