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

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Have you ever seen a person on the side of the road in a high visibility vest hunched over what looks like a camera on a tripod? Actually, this person is a surveyor and is looking through an instrument called a “theodolite”. A theodolite measures the angle between two points in space using degrees, minutes and seconds.

To locate key points the surveyor calculates the angles based on the blueprint numbers, then converts all the angles into DMS using scientific calculator.

Look for the DMS button on your calculator and try it out.

## Running with Pi

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3. Our Training Worksheets

Sometimes in your work you will need to convert an angle measured in decimal degrees to its equivalent in degrees and minutes. Example To convert 27.25° to degrees and minutes, follow these two steps:

1. Write the angle as a sum of a whole number and a decimal. 27°+ 0.25°
2. Multiply the decimal part by 60 to convert 0.25 to minutes

27.25°

= 27° + 0.25° × 60

= 27° + 15

= 27° 15

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

257.7261111° = 257° + (0.7261111x60) + (0.56666x60)” = 257° 43 34”

### 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 decimal degrees to DMS notation.
Remember the following key numbers:

Whole number degree amounts remain unchanged and copy over as degrees, followed by some minutes amounts as follows:

• 0.500 decimal degrees = 30 angular minutes
• 0.250 decimal degrees = 15 angular minutes
• 0.750 decimal degrees = 45 angular minutes
• 0.333 decimal degrees = 20 angular minutes
• 0.666 decimal degrees = 40 angular minutes

Example:

1. 25.500° =  ______”___°

### Worksheet: Level 1 Answer Key

1. 25.500° =  25°3000”

### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Questions

Question:

1. Convert 10.341666° degrees into DMS:

Further example:

1. Convert 37.1025° to DMS

### Worksheet: Level 2 Sample Answer Key

10.341666° → 10°

0.341666 × 60 = 20.5

0.5 × 60 = 30.00”

1. 10°2030.00”

Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

One 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: