 Hello and welcome to the session. In this session we shall discuss how to convert degree minute second measure into degree tenths that is decimal degrees and vice versa. Let us first understand the meaning of degree minute second measure that is DMS and decimal degree measure. First we have degree minute second measure that is DMS. Here the angles are often measured in degrees, minutes and seconds or decimal fractions of degrees. Now degrees, minutes and seconds are related by the following. Since 360 degrees is equal to one full rotation so one degree will be equal to 1 upon 360 of a full rotation. Also each degree is further divided into 60 equal parts called minutes that is one degree is equal to 60 minutes or one minute is equal to 1 by 60 degrees or we can also write it as one degree is equal to 60 minutes or one minute is equal to 1 by 60 degrees. Similarly each minute is further divided into 60 equal parts called seconds that is one minute is equal to 60 seconds or we can say one second is equal to one by 60 minutes or we can write it as one minute is equal to 60 seconds or one second is equal to one by 60 minutes. So degree measure expression is read as 23 degrees 45 minutes 15 seconds. Now we shall discuss decimal degrees. Now if we consider the following measure of angles that is 45.6 degrees 63.23 degrees 121.3 degrees. Here the measure is given in degrees only with a fractional part written in decimals. So these measures are the decimal degree measure of angles. Now to convert degree minute second measure into decimal degrees and vice versa we use the following results that is one degree is equal to 60 minutes or one minute is equal to one by 60 degrees and one minute is equal to 60 seconds or one second is equal to one by 60 minutes. Now let us see how to convert degree minute second into decimal degrees to convert degree minute second to decimal degree measure. We need to convert the minutes and seconds into degrees. Let us consider the following example convert 22 degrees 32 minutes 12 seconds into decimal degree measure. Here we are given this degree minute second measure which we have to convert into decimal degree measure. So first we will convert 32 minutes into degrees. We know that one minute is equal to one by 60 degrees so 32 minutes will be equal to 32 into one by 60 degrees. On solving this is equal to 0.533 degrees. Now again we shall convert 12 seconds into minutes and then into degrees. Now we know that one second is equal to one by 60 minutes and again converting one by 60 minutes into degrees we get one second will be equal to one by 60 into one by 60 degrees and this is equal to one upon 3600 degrees. Thus 12 seconds will be equal to 12 into one upon 3600 degrees. On solving this is equal to 0.0033 degrees thus we have converted 32 minutes and 12 seconds into degrees. Also we can write 22 degrees 32 minutes 12 seconds as 22 degrees plus 32 minutes plus 12 seconds and now putting the values of 32 minutes and 12 seconds in this we get 22 degrees plus 0.533 degrees plus 0.0033 degrees and this is equal to 22.5363 degrees. Thus we have written 22 degrees 32 minutes 12 seconds in decimal degree measure and this is the required decimal degree measure. Thus to convert degree minutes seconds into decimal degree measure we use the following results and these are one minute is equal to one by 60 degrees and one second is equal to one by 3600 degrees now we are going to discuss how to convert decimal degree measure into degree minute second. To do this conversion we will convert the decimal part of the given measure into minutes and seconds. Let us consider the following example convert 25.65 degrees into degree minute second. Here we are given 25.65 degrees which can be written as 25 degrees plus 0.65 degrees so here the decimal part is 0.65 degrees which will be converted into minutes. We know that one degree is equal to 60 minutes so we multiply the decimal part by 60 minutes so 25 degrees plus 0.65 degrees will be equal to 25 degrees plus 0.65 into 60 minutes and this is equal to 25 degrees plus now 0.65 into 60 minutes will be equal to 39 minutes and here we can see that minutes are not in decimals so we will not further convert it into seconds and this can be written as 25 degrees 39 minutes so 25.65 degrees is equal to 25 degrees 39 minutes which is the required degree minute second measure. We should note that while converting from decimal degree measure to degree minute second if we have a decimal part after converting into minutes then we further convert the decimal part in minutes in two seconds by using the result one minute is equal to 60 seconds so we multiply the decimal minute part by 60 seconds thus to convert decimal degree measure into degree minute second we use the following results that is one degree is equal to 60 minutes and one minute is equal to 60 seconds thus in this session we have discussed how to convert degree minute second to degree tens that is decimal degrees and vice versa this completes our session hope you enjoyed this session