Question

Express the angles in degree, minute and second
\[\left( a \right){{11.0133}^{\circ }}\]
\[\left( b \right){{94.3366}^{\circ }}\]

Answer 1

Hint: First of all, find the relation between the degree, minutes and seconds that is 1 degree = 60 minutes = 3600 seconds. Now multiply the given degree by 60 to find the minutes and further multiply it by 60 to find the seconds.

Complete step by step answer:
In this question, we are given angles in degrees and we have to convert them into the degree, minute and second or DMS system. We take the following steps to convert the decimal degrees to a degree, minute and second system.
(i) First of all, for degrees, we use the whole number part of the given angle in decimal degrees.
(ii) Now, for minutes, we will multiply the remaining decimal part by 60 and use the whole number part of the answer as the number of minutes.
(iii) Then, we will multiply the remaining decimal part of the minutes again by 60 and take the rounded-off figure of the answer as a number of seconds.
Now, let us consider the first part of the question.
\[\left( a \right){{11.0133}^{\circ }}\]
(i) We know that the whole number part is degrees. So, 11.0133 degrees gives us 11 degrees.
(ii) Now let us multiply the remaining decimal part that is 0.0133 degrees by 60 to get the minutes. So, we get,
\[0.0133\times 60=0.798\]
So, the whole number part, that is it has 0 minutes.
(iii) Now let us multiply the remaining decimal part that is 0.798 by 60 to get seconds. So, we get,
\[0.798\times 60=47.88\]
By rounding off 47.88, we get 48. So, we get 48 seconds.
Hence, we get, 11.0133 degrees = 11 degrees 0 minutes 47.88 or 48 seconds.
Now, let us consider the second point of the question.

\[\left( b \right){{94.3366}^{\circ }}\]
(i) We know that the whole number part is degrees. So, 94.3366 degrees gives us 94 degrees.
(ii) Now let us multiply the remaining decimal part that is 0.3366 by 60 to get the minutes. So, we get,
\[0.3366\times 60=20.196\]
So, the whole number part is, it has 20 minutes.
(iii) Now let us multiply the remaining decimal part that is 0.196 by 60 to get in seconds.
\[0.196\times 60=11.76\]
By rounding off 11.76, we get 12. So, we get 12 seconds.

Hence, we get 94.3366 degrees = 94 degrees 20 minutes and 11.76 or 12 seconds.

Note: Students must note that we could only round off the final answer that is the seconds’ part and not the degree or the minute’s part. Also, in this question students think that we need to convert the whole angle first into degrees, then into whole minutes and then into whole seconds which is incorrect because we need to convert an angle into a degree – minutes – seconds together.