In Exercises 19 to 24, use a calculator to convert each decimal degree measure to its equivalent

In Exercises 19 to 24, use a calculator to convert each...

Key Concepts

Decimal Degree Measure

A decimal degree measure represents an angle using degrees expressed in a base-10 format, which can include a fractional part. This representation is straightforward for computational purposes and is commonly used in digital applications for its simplicity.

Degrees, Minutes, and Seconds (DMS) Format

The DMS format breaks an angle into three parts: degrees, minutes, and seconds. One degree is divided into 60 minutes, and one minute is further divided into 60 seconds. This traditional format is often used in navigation, surveying, and mapping because it reflects a more human-friendly way of expressing angles.

Conversion Process

Converting a decimal degree measure to DMS involves separating the whole number, which represents the degrees, from the fractional part. The fractional degree is multiplied by 60 to obtain the minutes, and any remaining fraction is multiplied by 60 again to yield the seconds. This step-by-step process is essential for ensuring accuracy in the conversion.

Use of Calculators in Conversion

Calculators are commonly used in this conversion process to handle the multiplication and extraction of fractional parts accurately. They help in quickly computing minutes and seconds, especially when dealing with non-terminating decimals, thereby reducing manual calculation errors.

Transcript

00:03 All right.

00:04 And number 21, we want to convert the angle 64 .158 degrees to dms, which of course is degrees minutes and seconds.

00:16 Now, yes, this can be done very quickly by just using a graphing calculator.

00:24 They all have an angle menu built in, which certainly will have a conversion, you know, a dms.

00:34 Conversion capability.

00:37 But we're going to confirm our answer with the calculator instead because it's quick and easy to do by hand.

00:46 And otherwise there wouldn't be much instruction in this video, would there? it would just be push these buttons and there's your answer.

00:53 So i'll take a little more time and go through the process.

00:57 We already know the first part of our answer.

01:00 Right? 64 .158 degrees is going to be 64 degrees some number of minutes and some number of seconds.

01:09 So we already know the first part of our answer.

01:12 All we have to do is convert that 0 .158 degrees to minutes and then to seconds if necessary.

01:22 So that's quick and simple.

01:24 We're going to just take the fraction of the degree, 0 .158, we're going to multiply by 60, because there are 60 minutes in one degree, which you see written off to the right in green.

01:41 So 0 .158 times 60 gives me 9 .48.

01:47 So what that means is 158 ,000ths of one degree is 9 .48 minutes.

01:56 Now, if that were a whole number, we'd be done.

01:59 But we do know the second part of our answer.

02:02 It's nine minutes...

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