What is 45º 24' 30" ?

We know that angles are commonly measured in degrees,
and we have even seen angles expressed in decimal formats such as 16.5º and 120.25º.

There is an additional, and more precise, method of subdividing a degree
down into its smaller components which is commonly accepted.

In this method, the degree is divided into 60 equal parts called minutes. The minutes are further divided into 60 equal parts called seconds. Yes, these do sound familiar to the minutes and seconds that are used when speaking of time. And yes, these subdivisions are for the same amounts (60), but that is where the similarity ends.

Degrees, minutes and seconds are often used in relation to latitude and longitude.

45º 24' 30" is read 45 degrees, 24 minutes, 30 seconds.

Symbol for degree: º
Symbol for minute: '
Symbol for second: "
Calculator's Locations (TI-84 family):
º is under Angle (above APPS) #1
' is under Angle (above APPS) #2
" use ALPHA (green) key with quote symbol above + sign.


Change 45º 24' 30" to a decimal notation in degrees.

Mathematical Solution:
Calculator Solution:
Type 45º 24' 30" using calculator locations shown above. Hit ENTER.

Change 45.40833333 to degree, minutes, seconds.

Mathematical Solution:
We know the first entry will be 45º.
Find the number of minutes in the remaining 0.40833333 by dividing by 1/60. This gives 24 minutes with 0.4999998 of a minute remaining.
Find the number of seconds in the remaining 0.4999998 minutes by dividing by 1/60. This gives 29.999988 seconds, or 30 seconds.
Answer:  45º 24' 30''

This conversion missed by a slight amount on the exact seconds because 45.40833333 was an approximation of the original
45º 24' 30"
Calculator Solution:
Type 45.40833333 ►DMS Answer:  45º 24' 30''
 The ►DMS is #4 on the Angle menu (2nd APPS).  This function works even if Mode is set to Radian.

Convert 45º 24' 30" to radians.

Calculator Solution:
With the mode set to Radian:    Type 45° 24' 30'' º  and hit ENTER.
** Note the use of the additional degree symbol at the end.  Without it, conversion would be to decimal degrees, even though the mode is set to radians.
Answer: 0.7925249245


For help with radians and degrees on
your calculator,
click here.
MathBits Calculator Pages


NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation
and is not considered "fair use" for educators. Please read the "Terms of Use".