Significant Figures when Converting from DMS to Decimal Degrees

[deedsy]

Homework Statement

I converted 14:34:52.43 into decimal degrees which is 218.71845...

My question is, how do I know how many numbers I should write after the decimal to retain the original precision?

Homework Equations

1 hour = 15 degrees

The Attempt at a Solution

15 (14 + 34/60 + 52.43/3600) = 218.71845...

 

[deedsy]

I forgot to add, the coordinate I gave in my first post was originally in hours:minutes:seconds


An example in our lecture converted 45:00:30 (in DEGREES, minutes, seconds) to 45.008333. That means they used 8 significant figures for the decimal degree answer, but how did they determine that is how many they should use from 45:00:30?

 

[Borek]

Are you sure you are expected to watch sig figs?

To be on the safe side I would simply use the same number of digits after conversion. Please remember sig figs are rather lousy way of describing precision, and they are never worth too much effort.

 

[deedsy]

Are you sure you are expected to watch sig figs?

To be on the safe side I would simply use the same number of digits after conversion. Please remember sig figs are rather lousy way of describing precision, and they are never worth too much effort.

yes, after we convert the next question asks us how we determined the correct number of sig figs.

So my first guess was simply use 8, but that method isn't consistent with the example in our lecture. So next I just converted the entire thing to seconds and counting the sig figs and determined the decimal sig figs that way, but again, this method didn't work the example in our lecture

 

[deedsy]

I guess the question becomes, where does the 52.43 seconds fit into the decimal degrees' answer? The seconds are accurate to the hundredth decimal place, but where is that hundredth decimal place in relation to the decimal places contained in the decimal degree answer?

 

[gneill]

I guess the question becomes, where does the 52.43 seconds fit into the decimal degrees' answer? The seconds are accurate to the hundredth decimal place, but where is that hundredth decimal place in relation to the decimal places contained in the decimal degree answer?

The last digit in the given value can be assumed to embody the uncertainty in the given value, so if that digit should change a bit the uncertainty will be reflected in the conversion result.

Quick and dirty approach: Change the 52.43 seconds to 52.44 and then 52.42 (i.e. change the least significant digit in the starting value by +/- 1) and see which digits in the result change. Keep the unchanging digits plus one more. I think that should work for you.