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

The final example for converting decimal degrees to DMS uses 72.4813 degrees. This gives 72 degrees. Multiplying 0.4813 by 60 yields 28.878 minutes, so 28 minutes. Multiplying 0.878 by 60 gives 52.68 seconds, which is rounded up to 53 seconds due to the decimal part. The final answer is 72° 28' 53''. The importance of rounding and its effect on precision during verification is highlighted.

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Another conversion from decimal degrees to DMS is illustrated with 52.3175 degrees. This converts to 52 degrees. Multiplying 0.3175 by 60 gives 19.05 minutes, so 19 minutes. Then, multiplying 0.05 by 60 gives 3 seconds. The result is 52° 19' 3''.

The video begins by explaining how to convert degrees, minutes, and seconds (DMS) into a decimal in degrees. The analogy of an hour being equal to 1 degree, with 60 minutes in an hour and 3600 seconds in an hour, is used to facilitate understanding. The formula involves adding the degrees to the minutes divided by 60, plus the seconds divided by 3600. For example, 45° 28' 32'' converts to 45 + 28/60 + 32/3600, resulting in approximately 45.4756 degrees.

A second example demonstrates converting 38° 41' 27'' to a decimal in degrees. Following the formula, it becomes 38 + 41/60 + 27/3600, which calculates to approximately 38.6908 degrees when rounded to four decimal places.

A third example for DMS to decimal conversion is given: 53° 18' 39''. This is calculated as 53 + 18/60 + 39/3600, yielding approximately 53.3108 degrees.

The tutorial then switches to converting a decimal in degrees back into DMS. Using 38.4256 degrees as an example, the whole number (38) is the degree value. The decimal part (0.4256) is multiplied by 60 to find the minutes (25.536). The whole number of the result (25) is the minute value. The remaining decimal part of the minutes (0.536) is then multiplied by 60 to find the seconds (32.16), which is rounded to the nearest whole number (32) for the seconds value. The final result is 38° 25' 32''.

A quick check after converting decimal degrees to DMS is performed by converting the obtained DMS back to decimal degrees. This helps confirm the accuracy of the conversion, acknowledging that due to rounding, the result might be very close but not perfectly exact.