Which way is done correctly and why ??

Express the following in degrees,minutes, and seconds:

(1)4 --> (180/pi)*4 = 229.18312
229.18312 = 229 + (0.18312*60) = 229 degrees + 10.9872' = 229 deg 10' + (0.9872*60)" = 229 deg 10' + 59.2"

or

(2)4*180/pi = 229.18258
.18258*60=10.94548
.94548*60=56.7288

299deg 10' 56"

I'm not sure if my calculation was wrong or if i didn't round the numbers , so i don't how the first way(example way)came up with different answers then the second way (my calcutations).

To express a value in degrees, minutes, and seconds, you can use two different methods:

(1) The first method involves converting the given value to decimal degrees, then separating the decimal degrees into whole degrees, minutes, and seconds.

Using your example of 4 degrees:

Step 1: Convert 4 degrees to decimal degrees:
4 degrees = (180/pi) * 4 ≈ 229.18312

Step 2: Separate the decimal degrees:
Since 1 degree = 60 minutes, we can multiply the decimal value after the whole degrees by 60 to get the minutes.

0.18312 * 60 = 10.9872

So, we have 229 degrees and 10.9872 minutes.

Step 3: Further separate the minutes:
Again, since 1 minute = 60 seconds, we can multiply the decimal value after the whole minutes by 60 to get the seconds.

0.9872 * 60 = 59.2

Therefore, the final answer is 229 degrees, 10 minutes, and 59.2 seconds, which can be represented as 229° 10' 59.2".

(2) The second method involves converting the given value to decimal degrees and then directly separating it into degrees, minutes, and seconds without rounding at each step.

Using your example of 4 degrees:

Step 1: Convert 4 degrees to decimal degrees:
4 degrees = 4 * (180/pi) ≈ 229.18258

Step 2: Separate the decimal degrees:
Separate the decimal part into degrees, minutes, and seconds without rounding:

0.18258 * 60 = 10.94548

0.94548 * 60 = 56.7288

Therefore, the final answer is 229 degrees, 10 minutes, and 56.7288 seconds, which can be represented as 229° 10' 56.7288".

So, in your calculations, it seems that rounding the value at each step in Method 1 caused the discrepancy between the two methods. The second method, without rounding until the final step, gives a more accurate representation of the value in degrees, minutes, and seconds.