How Do You Convert Degrees Into Fractions?

3 Answers

Iris Phillips Profile
Iris Phillips answered
Degrees and their fractions are usually represented in so-called degrees, minutes and seconds, such as 25º 30 minutes 27 seconds, for instance. To convert degrees to fractions, it is essential to know that each minute is expressed as 1/60 of a degree, while each second is expressed as1/60 of a minute, or 1/3600 of a degree.

  • The Conversion
Nothing needs to be done with the 25º, as these are whole degrees. The 30 minutes equal 30/60 of a degree and the seconds equal 27/3600 of a degree. We consequently have 25º + 30/60 + 27/3600.

To combine these two separate fractions, we have to find a common denominator. To avoid involving decimal places by dividing the 30/3600 by 60 to make the common denominator 60, we make the common denominator 3600 by multiplying 30/60 by 60. This now gives us 25º + 1800/3600 + 27/3600, or 25º + 1827/3600.

The 1827/3600 can be reduced by dividing each number with a common denominator, which in this case is 9. The new fraction is then 203/400, giving us 25º + 204/400, or 25º 203/400.

To express this as a decimal version, the 203 is divided by 400, giving 0.5075, which makes the angle 26.5075º.

If the original angle had been 25º 30 minutes 0 seconds, for instance, the fraction would have been 25 1800/3600º, which could have been reduced to 25 1/2º or 25.5º.

An original angle of 25º 30 minutes 57 seconds would equal 25 1857/3600º. As there is no common denominator for 1857 and 3600, it can not be reduced. Expressed in decimals, the angle would be 25.5158333333º.

This example was given to show that the actual figures ultimately determine how far a fraction can be reduced.
Oddman Profile
Oddman answered
If you want fractions of a whole circle, divide by 360°.

Example
90° = (90°)(1 circle/360°) = (90/360) circle = 1/4 circle

If you want radians, multiply by Pi/180°.

Example
60° = (60°)(Pi radians/180°) = Pi(60/180) radians = Pi/3 radians

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