Converting Angles Between Degrees and DMS (Degrees, Minutes, Seconds)

Introduction

• Objective: Learn how to convert angles between degrees and DMS format.
• Units:
  • One minute = 1/60th of a degree.
  • One second = 1/60th of a minute = 1/3600th of a degree.
  • Notation:
    • Degrees (D) - °
    • Minutes (M) - '
    • Seconds (S) - "

Conversion from DMS to Decimal Degrees

1. Problem: Convert 40° 10' 25" to decimal degrees.
2. Steps:
   • Degrees: Already in desired unit, remain as 40°.
   • Convert Minutes:
     • 10 minutes × 1/60 = 1/6 degree.
   • Convert Seconds:
     • 25 seconds × 1/3600 = 1/144 degree.
3. Combine:
   • Add all parts: 40° + 1/6° + 1/144°.
   • Result: 40 + 0.1667 + 0.0069 (approximately).
   • Final answer: 40.17° (rounded to two decimal places).

Conversion from Decimal Degrees to DMS

1. Problem: Convert 61.24° to degrees, minutes, and seconds.
2. Steps:
   • Break Down:
     • 61.24° = 61° + 0.24°.
   • Convert Decimal to Minutes:
     • 0.24° × 60 = 14.4 minutes.
   • Convert Decimal Minutes to Seconds:
     • 0.4 minutes × 60 = 24 seconds.
3. Combine:
   • 61° + 14' + 24".
   • Final DMS representation: 61° 14' 24".

Additional Notes

• Rounding: Ensure rounding to the required decimal places for clarity and accuracy.
• Multiplication Factors:
  • Degrees to Minutes: ×60.
  • Minutes to Seconds: ×60.
  • Use accurate unit conversions to avoid mistakes.

Conclusion

• Practice converting between these units to become proficient.
• Understand reciprocal relationships between conversion formulas for both directions.