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Converting DMS to Decimal Degrees
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1. Our Training Videos
Skills Application: Converting Degrees Minutes and Seconds to Decimal Degrees
Step-by-Step: Converting Degrees Minutes and Seconds to Decimal Degrees
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2. Running with Pi ## Tagged in

When carpenters are planning to build a circular stair they need to think in terms of time! How does time relate to cutting stairs? Well, math with time and angles are both based on the number 60. To produce a high level of precision for each cut, tread angles are carefully calculated in degrees-minutes-and-seconds. In the course of subsequent calculations the tread angles are converted from degrees, minutes and seconds to decimal degrees. The decimal degrees are then used in chord calculations. The treads edge and its chords are easily laid out for those precise cuts. Ta-da! The perfect start for the perfect stairs.

## Converting Degrees Minutes and Seconds to Decimal Degrees ## Running with Pi  . . . . . . . . .
3. Our Training Worksheets

Sometimes in your work you will need to convert an angle measured in degrees and minutes to its equivalent in decimal degrees.

To convert the angle 4°30 to decimal form follow these two steps:

1.    Write the angle as a sum of degrees and minutes

4°30= 4°+ 30

2.  Use a 60-base fraction to convert minutes to degrees.

$\text{4° 30′ = 4° + (}\frac{30′}{60′}\text{)}$

= 4°+ 0.5°

= 4.5°

Get a $20-or-so dual-display scientific calculator, even if you cant take it with you into the exam hall. A calculator is also a learning tool, Technology Use is one of the 9 Essential Skills you cant do without. Trying out different functions on a calculator will further your understanding and help with building a bigger mental picture. It builds links between numbers and algebra. It is important to try alternative calculations or approaches, to sketch & label angles, tracking changes to units of measure, visualizing to cross-link the concepts of angles and numbers. ### A Short Review $\text{35° 56′ 37″ = 35 + }\frac{56}{60}+\frac{37}{3600}$ = 35.94361111° ### Worksheet: Level 1 The operations used are clearly specified. Only one type of mathematical operation is used in a task. ### Worksheet: Level 1 Sample Questions Write the following amounts in DMS notation as decimal numbers. Remember the following key numbers: Degree amounts remain unchanged and copy over as whole numbers, followed by some decimal digits: 30 angular minutes = 0.500 decimal degrees 15 angular minutes = 0.250 decimal degrees 45 angular minutes = 0.750 decimal degrees 20 angular minutes = 0.333 decimal degrees 40 angular minutes = 0.666 decimal degrees Example: 1. 25°15‵00" = ______° Further example: 1. Convert 27” to decimal degrees. ### Worksheet: Level 1 Answer Key Answer: 25°15‵00" = 25.250° ### Download Worksheet: Level 1 ### Worksheet: Level 2 Tasks involve one or two types of mathematical operation. Few steps of calculation are required. ### Worksheet: Level 2 Sample Questions Convert to decimal degrees. Answer to 6 decimal places. Example: 1. Convert 20°3030” into decimal degrees: Further example: 1. Convert 28°3529.03” into decimal degrees. ### Worksheet: Level 2 Sample Answer Key Answer: 20° → 20.000000° 30′ ÷ 60 = 0.500000° 30" ÷ 3600 = 0.008333° 20.00° + 0.50° + 0.008333° = 20.508333° ### Download Worksheet: Level 2 ### Infosheet: Advanced Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required. ### Additional Information: Another Way to Get the Answer Task: Convert 37°1508” to decimal degrees. Another Way to Get the Answer Layout your calculations neatly, so you can review, track changes, correct or learn from them. One way a layout can look is like this: ### Additional Information: Another way to get the answer, using a scientific calculator Task: Convert 37°1508” to decimal degrees. Another way to get the answer, using a scientific calculator: 1. Enter 37 DMS 15 DMS 8 DMS 2. Press 2ndF 3. Press DMS Take a pencil and write down 37.252222 4. The number on the display changes to 37.25222222 5. Write the ° sign after the 37.252222 Now youre done with the math. 6. The last step is to check your work: make sure everything was copied and written correctly then determine that the correct way to write the answer is 37.252222 ### Additional Information: Another way to get the answer, using a scientific calculator and bracketing Task: Convert 37°1508” to decimal degrees. Another way to get the answer, using a scientific calculator and bracketing: It is possible to enter everything in the calculator in one line. Get a$20-or-so dual-display scientific calculator, even if you cant take it with you into the exam hall. A calculator is also a learning tool, Technology Use is one of the 9 Essential Skills you cant do without.

Here are the steps with some explanations:

1. Identify that 37°1508” is an angle in DMS.
2. Identify that the angle 37°1508” needs to be converted to decimal degrees.
3. Recognize that ° means degrees,  means minutes and means seconds.
4. Recognize that the degrees amount in the DMS number is the exact degrees amount in decimal degrees. Theres no math with it, it stays unchanged, 37.
5. Recognize that the minutes amount needs converting to degrees. Recognize that the conversion factor to convert from minutes to degrees is 60, since there are 60 minutes in a degree.
6. Recognize that to convert from DMS to decimal degrees the conversion factor will be a divisor because many of the smaller unit are to be shared equally by groups of the bigger unit. (Look at the minutes amount. 15 minutes is not 15 degrees, 15 minutes is smaller than 1 degree, its gonna be zero-point-something degree)
7. Recognize that the seconds amount also needs converting to degrees. Recognize that the conversion factor to convert from seconds to degrees is 3600, since there are 3600 seconds in a degree. (60 seconds x 60 minutes = 3600 seconds in a degree)
8. Recognize that to convert from DMS to decimal degrees the conversion factor will be a divisor again because many of the smaller unit are to be shared equally by groups of the bigger unit.
9. Set up the problem:
10. degrees + minutes as decimal degrees + seconds as decimal degrees = angle in decimal degrees.
Calculate: 37   +    (15 ÷ 60)    +    (8 ÷ 3600)    =    37.252222
11. Take a pencil and write down  37.252222
12. Write the ° sign after the 37.252222 Now you`re done with the math.
13. The last step is to check your work: make sure everything was copied and written correctly then determine that the correct way to write the answer is 37.252222°