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Question Video: Converting an Angle Expressed in Degrees, Minutes and Seconds to Only Degrees Using a Calculator Mathematics

Using a calculator, write 25° 30′ 45″ in degrees.

03:46

Video Transcript

Using a calculator, write 25 degrees, 30 minutes, and 45 seconds in degrees.

We recall that the single quotation mark for the number in the question stands for minutes and the double quotation mark stands for seconds. We also know that there are 60 minutes in one degree. In turn, a minute is made up of 60 seconds. We need to work out how we can use this information to convert 25 degrees, 30 minutes, and 45 seconds into just degrees. One way is to consider all three parts separately. We know that we have 25 full degrees. As one degree is equal to 60 minutes, one minute will be equal to one sixtieth of a degree. We can, therefore, convert 30 minutes into degrees by multiplying 30 by one sixtieth. This is the same as dividing 30 by 60.

In the same way, one second is equal to one sixtieth of a minute. We can, therefore, convert 45 seconds into degrees by multiplying 45 by one sixtieth and then by one sixtieth again. A quicker way to do this would be to recognize that as 60 multiplied by 60 is 3600, then one second is equal to one three thousand six hundredths of a degree. We can, therefore, convert 45 seconds into degrees by multiplying 45 by one over 3600. This is the same as 45 divided by 3600. 30 divided by 60 is equal to 0.5. 45 divided by 3600 is 0.0125. Adding these two answers together with 25 gives us 25.5125. 25 degrees, 30 minutes, and 45 seconds is equal to 25.5125 degrees.

There is a quicker way of doing this in one step on the calculator. This involves using the degrees, minutes, and seconds button that can be found on the majority of scientific calculators. We begin by inputting the number 25. We then press our button. We input 30 followed by the button again. Finally, we input 45 and the button a third time. When we press the equals button, the number 25 degrees, 30 minutes, and 45 seconds will appear on our calculator display. We then need to press the degrees, minutes, and seconds button a final time, which will give us the answer 25.5125. This is the answer that we calculated earlier in degrees.

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