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Multiplying DMS
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Skills Application: Multiplying Degrees, Minutes and Seconds
Step-by-Step: Multiplying Degrees, Minutes and Seconds
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Pilots rely on an accurate navigational system to find their way around in any weather. If the navigational system is inaccurate by a few arc minutes; this assumingly tiny error over the length of the flight multiplies by hundreds of times and completely alters the course of the plane. Such was the case in the 1996 Croatian crash of USAF flight IFO-21.

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Sometimes in your work you will need to multiply angles in degrees and minutes. Multiplication works the same way as it does with whole numbers. There is only one difference: Carrying over is done in multiples of 60 between the degrees, minutes or seconds columns, but it is done in multiples of 10 within a column. Watch the video and see.

A Short Review

To multiply 5° 20 30” by 3, carrying is necessary from the seconds to minutes and minutes to degrees. Carrying within the minutes and seconds column is 10-based, carrying between columns is 60-based.

30” x 3 = 90”, but 60” of this is carried to the minutes column, where it shows up as a 1

20 x 3 = 60, but this carries over to the degrees column where it shows up as 1°.

5° 20 30” = 5° 60 90” = 16° 1 30”

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

1. Decide whether carrying-over is needed in the following multiplications in DMS and;
2. Specify where exactly carrying is needed, if any:

Remember:

Multiply mentally or estimate the subtotals of the seconds and minutes units and decide if a subtotal is more or less than 59 or 59.99 If more, carrying over will be needed to the next column to the left.

25° 10 25.11” × 2   > No carrying is needed.

25° 10 25.11” × 3   > Carrying is needed from seconds to muinutes.

Example:

1. 54° 14 29.27” x 2 =

Further examples:

1. If 28.253 gets multiplied by 2, will carrying over be needed?

No carrying is needed.

Worksheet: Level 2

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

Worksheet: Level 2 Sample Questions

Example:

Multiply in DMS:

Question:

1. 26° 37 29.92” x 5 =

Further examples:

Multiply 54° 33 43.23” x 3 ½ =

Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

Worksheet: Level 3 Sample Questions

Example:

Multiply in DMS:

Question:

1. A cabinetmaker is trying to make a full inlaid circle of 68 pieces of alternating tapered slices of black walnut and spruce veneer. What is the total angle of turn if each slice has an angle of
5° 21 ?

Further example:

1. What is the total turn of a segmented elbow of a pipe if 4 sections are joined, each with a turn of 4° 27 45.67”?

Worksheet: Level 3 Sample Answer Key

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

Another Way to Get the Answer

What is the total angle of turn of 3 tapered pieces, each with an angle of 26° 21 28.44”?

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

Another way to get the answer, using a scientific calculator:

Enter 26 DMS 21 DMS 28.44 DMS

Press x (multiply)

Enter 3

Press =

The number on the display changes to 79° 4 25.32”

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 can`t do without.