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...

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Key Concepts

Decimal Degrees

This concept refers to an angle measurement expressed in a single numerical value with a decimal component to represent fractions of a degree. It is a standard form used in many applications, such as geography and navigation, following the base-10 numeral system.

Degrees, Minutes, and Seconds (DMS)

The DMS system breaks down an angle into three parts: whole degrees, minutes (where 1 degree equals 60 minutes), and seconds (where 1 minute equals 60 seconds). This method provides a more precise representation of angles by separating the fractional component of a degree into smaller units.

Conversion Process

Converting a decimal degree to DMS involves separating the whole number part as the degree component, multiplying the fractional part by 60 to obtain minutes, and then multiplying the remaining fractional part of the minutes by 60 to get seconds. This systematic process allows for an exact conversion from a base-10 measurement to a traditional sexagesimal format.

Rounding Procedures

When converting decimal degrees to DMS, rounding is often necessary, particularly for the seconds component, to match the desired precision. Using a calculator facilitates accurate multiplication and rounding, ensuring the converted angle meets the required level of detail.

Transcript

00:02 And number 20, we're given an angle in degrees, and we are asked to convert to degrees, to degrees, minutes, and seconds.

00:14 Now, yes, this can be done very quickly on the calculator.

00:19 In fact, they're telling us to use a calculator, but that's no fun just pushing a couple buttons.

00:25 So let's talk about how we would do it by hand real quick.

00:32 Okay? we already know the first part of our answer is 110 degrees.

00:37 What we need to figure out is how many minutes and how many seconds are made up by this point two, four.

00:44 And it's a very simple process because you recall that one minute is, i'm sorry, one degree.

00:55 Let's start with that one.

00:56 One degree is 60 minutes and one minute is 60 seconds.

01:00 So all we have to do is a couple steps of multiplication here.

01:05 To find the number of minutes in 0 .24 degrees, simply multiply 0 .24 degrees by 60.

01:14 Oops, that's 60.

01:17 There we go.

01:20 And that'll be the number of minutes in 0 .24 of a degree.

01:26 And if that's a whole number, then your answer is done, because then there will just be 0 seconds.

01:32 Okay.

01:33 But if you do that multiplication, you're going to get 14 .4...

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