Question Video: Converting an Angle Expressed in Degrees, Minutes and Seconds to Only Degrees Without Using a Calculator Mathematics

Without using a calculator, write 20° 30′ 45″ in degrees.


Video Transcript

Without using a calculator, write 20 degrees, 30 minutes, 45 seconds in degrees.

We recall that the quotation mark symbols in the question represent minutes and seconds, respectively. There are 60 minutes in one degree. This means that in order to convert from minutes to degrees, we need to divide by 60. Likewise, there are 60 seconds in one minute. 60 multiplied by 60 is 3600. Therefore, this is the number of seconds in one degree. To convert from seconds to degrees, we need to divide by 3600. We need to write the three parts of our original number separately.

We begin with 20 degrees. We then have 30 minutes, which in degrees would be 30 divided by 60 or 30 over 60. We then have 45 seconds, which can be converted into degrees by dividing by 3600. The first fraction simplifies to three over six and then one-half. One-half is equal to 0.5. So, 30 divided by 60 is 0.5. We know that 45 multiplied by eight is 360. This means that 45 multiplied by 80 is 3600. So, our second fraction simplifies to one over 80 or one eightieth. We recall that one-eighth is equal to 0.125. It is half of a quarter. Dividing this by 10 gives us that one eightieth is equal to 0.0125. Adding these three values gives us 20.5125. We can, therefore, conclude that 20 degrees, 30 minutes, and 45 seconds is the same as 20.5125 degrees.

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