 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that first, convert 74.125 degrees into degree minute second measure. Second, convert 46 degrees 52 minutes 38 seconds into decimal degree measure. Before starting the solution of this question we should know some results and these are to convert decimal degrees into degree minute second. We will convert the decimal part of the given measure into minutes and seconds by using the following results that is 1 degree is equal to 60 minutes and 1 minute is equal to 60 seconds. Also we have to convert degree minute second into decimal degree measure. We need to convert the minutes and seconds into degrees by using the following results that is 1 minute is equal to 1 by 60 degrees and 1 second is equal to 1 by 3600 degrees. With this key idea we shall move on to the solution. In the first part of the question we have to convert 74.125 degrees into degree minute second measure. For this we will convert the decimal part of the angle into minutes and seconds. We are given 74.125 degrees which can be written as 74 degrees plus 0.125 degrees. So here the decimal part is 0.125 degrees which will be converted into minutes. Now using the key idea we know that 1 degree is equal to 60 minutes. So we multiply the decimal part by 60 minutes. So 74.125 degrees will be equal to 74 degrees plus 0.125 into 60 minutes and this is equal to 74 degrees plus 0.125 into 60 is 7.5 minutes. Now here we see that minutes are in decimals. So we will further convert the decimal part of minutes into seconds. Now we can further write it as 74 degrees plus 7 minutes plus 0.5 minutes and we know that 1 minute is equal to 60 seconds. So we multiply 0.5 minutes by 60 seconds and we get 74 degrees plus 7 minutes plus 0.5 into 60 seconds and this is equal to 74 degrees plus 7 minutes plus 30 seconds which can be written as 74 degrees 7 minutes 30 seconds. Thus 74.125 degrees is equal to 74 degrees 7 minutes 30 seconds. This is the required angle measure in degree minutes second. This is the required answer to the first part of the question. Now we move on to the second part of the question which says convert 46 degrees 52 minutes 38 seconds into decimal degree measure. Now here we are given 46 degrees 52 minutes 38 seconds and this can be written as 46 degrees plus 52 minutes plus 38 seconds. So now we will convert 52 minutes and 38 seconds into degrees using these results given in the key idea. So now we will multiply 52 minutes by 1 by 60 degrees and 38 seconds by 1 upon 3600 degrees to convert these into degrees. So we get 46 degrees plus 52 into 1 by 60 degrees plus 38 into 1 by 3600 degrees. On solving this further we get 46 degrees plus 0.866 degrees plus 0.0105 degrees. On adding these we get 46.8765 degrees. So 46 degrees 52 minutes 38 seconds is equal to 46.8765 degrees which is the required answer in decimal degree measure. This completes our session. Hope you enjoyed this session.