Decimal Degrees to DMS Formula - Converting Degrees Minutes and Seconds to Decimal - Trigonometry

The Organic Chemistry Tutor
18 Jun 201711:57
EducationalLearning
32 Likes 10 Comments

TLDRThe video tutorial explains how to convert degrees, minutes, and seconds (DMS) into decimal degrees and vice versa. It provides step-by-step instructions with examples, showing how to perform the conversions using basic arithmetic and a calculator. Additionally, the video covers common pitfalls and rounding techniques to ensure accurate results. The instructor also mentions an online trigonometry course available on Udemy, which includes various topics like angle conversion, trigonometric functions, and problem-solving strategies. The course aims to provide comprehensive knowledge and practice in trigonometry.

Takeaways
  • 📚 The script explains how to convert degrees, minutes, and seconds (DMS) into decimal degrees.
  • 🕒 It uses the analogy of an hour to help remember the conversion process, with 1 degree equivalent to 1 hour, 60 minutes in an hour, and 3600 seconds in an hour.
  • 🔢 The conversion formula for DMS to decimal degrees is: Degrees + (Minutes / 60) + (Seconds / 3600).
  • 📈 An example is given with the value 45 degrees, 28 minutes, and 32 seconds, which converts to 45.4756 degrees.
  • 📝 Additional examples are provided to demonstrate the conversion process, including rounding to four decimal places where necessary.
  • 🔄 The script also covers converting a decimal degree value back into DMS format.
  • 📐 The method for converting decimal degrees to DMS involves multiplying the decimal part by 60 to find minutes and then further multiplying the remaining decimal by 60 to find seconds.
  • 📲 To confirm the conversion, the original and converted values are recalculated to ensure they are close to the original value.
  • 🧭 The importance of rounding and the impact of rounding on the accuracy of the conversion is discussed.
  • 📚 The script mentions an online trigonometry course available on Udemy, covering various topics from basics to advanced concepts.
  • 🔗 A direct link to the course on Udemy is provided for those interested in a comprehensive study of trigonometry.
Q & A

  • What is the basic concept for converting degrees, minutes, and seconds (DMS) to decimal degrees?

    -The basic concept involves treating an hour as equal to one degree, with 60 minutes in one hour and 3600 seconds in an hour. This helps in remembering the conversion process: degrees plus (minutes divided by 60) plus (seconds divided by 3600).

  • How do you convert 45 degrees, 28 minutes, and 32 seconds into decimal degrees?

    -You would calculate it as 45 + (28/60) + (32/3600), which equals approximately 45.4756 degrees.

  • What is the result when converting 38 degrees, 41 minutes, and 27 seconds into decimal degrees?

    -The result is 38 + (41/60) + (27/3600), which equals approximately 38.6908 degrees when rounded to four decimal places.

  • How is the conversion of 53 degrees, 18 minutes, and 39 seconds into decimal degrees calculated?

    -The calculation is 53 + (18/60) + (39/3600), resulting in approximately 53.3108 degrees.

  • What is the process for converting a decimal degree value back into DMS?

    -First, identify the whole number as the degrees. Then, multiply the decimal part by 60 to get minutes, and take the whole number part of the result. For the remaining decimal, multiply by 60 again to get seconds, rounding to the nearest whole number if necessary.

  • How do you convert 38.4256 degrees into DMS?

    -First, take the whole number 38 as degrees. Multiply the decimal 0.4256 by 60 to get 25.536, take the whole number 25 as minutes. Multiply the remaining decimal 0.536 by 60 to get 32.16, and round to 32 seconds, resulting in 38 degrees, 25 minutes, and 32 seconds.

  • Why might the conversion from decimal degrees back to DMS not be exact?

    -The conversion might not be exact because of rounding during the process, such as rounding 32.16 to 32 seconds.

  • What is the process for confirming the accuracy of a DMS to decimal degree conversion?

    -To confirm accuracy, reconvert the DMS back to decimal degrees using the original formula and compare it to the original decimal degree value. The result should be very close to the original value.

  • How do you convert 52.3175 degrees into DMS?

    -First, take the whole number 52 as degrees. Multiply the decimal 0.3175 by 60 to get 19.05, take the whole number 19 as minutes. Multiply the remaining decimal 0.05 by 60 to get 3 seconds, resulting in 52 degrees, 19 minutes, and 3 seconds.

  • What happens when converting 72.481 degrees into DMS, and why should you be careful with rounding?

    -First, take the whole number 72 as degrees. Multiply the decimal 0.481 by 60 to get 28.878, take the whole number 28 as minutes. Multiply the remaining decimal 0.878 by 60 to get 52.68, and round to 53 seconds. Be careful with rounding because it can affect the accuracy of the conversion back to decimal degrees.

  • Where can one find the complete online trigonometry course mentioned in the script?

    -The complete online trigonometry course can be found on Udemy.com by searching for 'trigonometry' in the search box. The course has a black background and includes various topics such as angles, converting degrees into radians, linear and angular speed problems, arc length, unit circle, trigonometric functions, right triangle trigonometry, graphing sine and cosine functions, and more.

Outlines
00:00
📚 Converting DMS to Decimal Degrees

This paragraph explains the process of converting degrees, minutes, and seconds (DMS) into a decimal format of degrees. The instructor likens an hour to one degree and emphasizes that there are 60 minutes in an hour and 3600 seconds in an hour to aid in memory. An example is given where 45 degrees, 28 minutes, and 32 seconds are converted to decimal degrees by adding the degree value and dividing the minutes and seconds by 60 and 3600, respectively. The result is 45.4756 degrees. Additional examples are provided, including converting 38 degrees, 41 minutes, and 27 seconds to 38.6908 degrees, and 53 degrees, 18 minutes, and 39 seconds to approximately 53.3108 degrees.

05:00
🔄 Converting Decimal Degrees to DMS

The second paragraph focuses on converting a decimal degree value back into degrees, minutes, and seconds (DMS). The example of 38.4256 degrees is used to demonstrate this conversion. The whole number represents the degrees, and the decimal is multiplied by 60 to find the minutes. The remaining decimal is then multiplied by 60 to find the seconds, which are rounded to the nearest whole number. The result is 38 degrees, 25 minutes, and 32 seconds. The paragraph also discusses the importance of checking the conversion accuracy by recalculating the original decimal value from the converted DMS, noting that rounding may lead to slight inaccuracies.

10:01
🎓 Online Trigonometry Course Information

In the final paragraph, the instructor provides information about an online trigonometry course available on Udemy. The course is described as comprehensive, covering topics such as angles, converting degrees to radians, linear and angular speed problems, arc length, unit circle, trigonometric functions, right triangle trigonometry, word problems, graphing sine and cosine functions, secant, tangent, inverse trig functions, bearings, verifying trigonometric identities, and more. The instructor mentions ongoing updates and additions to the course content and encourages viewers to check it out.

Mindmap
Keywords
💡DMS (Degrees, Minutes, Seconds)
DMS stands for Degrees, Minutes, and Seconds, which is a way of expressing angles. In this method, degrees are divided into 60 minutes, and each minute is further divided into 60 seconds. This concept is crucial in the video as it teaches how to convert between DMS and decimal degrees. For instance, the video explains how to convert 45 degrees, 28 minutes, and 32 seconds into decimal degrees.
💡Decimal Degrees
Decimal degrees represent angles using a decimal format rather than degrees, minutes, and seconds. This is useful for simplifying calculations and is often used in fields like cartography and navigation. The video illustrates converting DMS to decimal degrees using examples such as 45 degrees, 28 minutes, and 32 seconds being converted to 45.4756 degrees.
💡Conversion Formula
The conversion formula is a mathematical expression used to convert DMS to decimal degrees. The formula involves dividing the minutes by 60 and the seconds by 3600, then adding these values to the degrees. For example, 45 degrees, 28 minutes, and 32 seconds convert to decimal degrees by calculating 45 + (28/60) + (32/3600).
💡Minutes
In the context of angles, a minute is 1/60th of a degree. Minutes are used as an intermediate unit between degrees and seconds. The video highlights the conversion process by dividing the number of minutes by 60 to integrate them into the decimal degree format.
💡Seconds
Seconds are 1/60th of a minute and 1/3600th of a degree. They are the smallest unit in the DMS system. The video demonstrates that to convert seconds into decimal degrees, you divide the number of seconds by 3600. For example, 32 seconds divided by 3600 contributes to the overall decimal degree calculation.
💡Rounding
Rounding is the process of approximating a number to a specified degree of precision. In the video, rounding is used to simplify results, such as rounding 32.16 to 32 seconds. This step is important to provide a manageable and accurate representation of the converted values.
💡Verification
Verification involves checking the accuracy of the converted values by reversing the conversion process. The video emphasizes verifying conversions by re-calculating from decimal degrees back to DMS to ensure consistency and correctness, as shown in multiple examples.
💡Calculator
A calculator is a tool used to perform arithmetic operations required for conversions. The video frequently instructs viewers to use their calculators to input formulas and get precise decimal degree values, demonstrating how practical tools are essential in the conversion process.
💡Examples
Examples are specific problems used to illustrate and practice the conversion processes. The video provides several examples, such as converting 38 degrees, 41 minutes, and 27 seconds to 38.6908 degrees, which helps viewers understand and apply the conversion methods.
💡Udemy
Udemy is an online learning platform mentioned in the video, where the instructor's trigonometry course is hosted. The mention of Udemy contextualizes the video as part of a broader educational offering, encouraging viewers to explore more structured and comprehensive learning resources.
Highlights

Introduction to converting degrees, minutes, and seconds (DMS) into decimal degrees.

Understanding that an hour is equivalent to one degree, with 60 minutes and 3600 seconds in an hour.

Conversion method: Add degrees, divide minutes by 60, and divide seconds by 3600.

Example calculation: Convert 45 degrees, 28 minutes, and 32 seconds to 45.4756 degrees.

Conversion of 38 degrees, 41 minutes, and 27 seconds to decimal degrees, rounded to four decimal places.

Conversion of 53 degrees, 18 minutes, and 39 seconds to approximately 53.3108 degrees.

Reversing the process to convert decimal degrees back into DMS.

Conversion of 38.4256 degrees into DMS resulting in 38 degrees, 25 minutes, and 32 seconds.

Verification of conversion accuracy by recalculating the original value.

Conversion of 52.3175 degrees into DMS resulting in 52 degrees, 19 minutes, and 3 seconds.

Conversion of 72.481 degrees into DMS with rounding considerations.

Explanation of rounding impact on conversion accuracy.

Introduction to an online trigonometry course available on Udemy.

Course content includes various trigonometry topics such as angles, radians, linear and angular speed, arc length, unit circle, and trigonometric functions.

Course also covers right triangle trigonometry, word problems, graphing functions, inverse trig functions, and trigonometric identities.

Mention of ongoing updates and additions to the course content.

Transcripts

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