Sig Figs: Displacement of Car from Origin - 2.8x10^2 km?

[ThomasMagnus]

How many sig figs would be in the final answer of the following question.

A car is driven 215 km west and then 85km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

Now in the book they list the answer as 282km and 12 degrees south of west.

Should the answer to the correct number of significant digits be 2.8x10^2 km? Reason being the 85 is limiting the final answer to 2 sig figs. It seems to be done correctly for the angle, it is 2 sig figs.

Am I missing something here, or is there a mistake in the book?


So is it step by step or is the whole question limited to 2 sig figs by the given data (85) and is it always like this?



Thanks!

 

[tiny-tim]

Hi Thomas!

How many sig figs would be in the final answer of the following question.

A car is driven 215 km west and then 85km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

hmm … it it was 215 km west and then 1 km southwest, would you say the answer was 200 km?

(but, sorry, I've no idea what the logical explanation is )

 

[Borek]

The only logical explanation I can think of is... significant digits are a faulty concept.

 

[ThomasMagnus]

Regardless of the question. The given data was 215 and 85. Shouldn't the final answer then have 2 sig figs? I think they may have just put three to avoid scientific notation.
The final answer in the book is 282(three sig figs) I'm thinking it should be 2.8x10^2

 

[Borek]

Not necessarily. 1000+1 is not 1e3, rules for addition and subtraction are slightly different.

 

[ThomasMagnus]

For adding and subtracting its the least number of decimal places.

My question is when you get a problem that, for examples, gives you the numbers 215 and 85. These are the givens, how you get to the final answer doesn't matter here. Right away when you see a question's givens, are you supposed to determine that the lowest number of sig figs in the givens is the # of sig figs they want in the final answer?

Thanks

 

[Borek]

As I wrote earlier - SF are a faulty way of expressing accuracy, so I would not care too much.

I have asked your question (slightly modified - 999 km north, then 9, 99 or 999 km east) somewhere else, that's the best answer I got (thanks JB):

I'm going to apply the following rules:
1) When multiplying or dividing, round to the lowest number of sig figs.
2) When adding or subtracting, round to the lowest number of decimal places (or to the tens or hundreds place as necessary).
3) Don't round your final answer until the end but track how many sigfigs each intermediate simple step should produce and use that for the subsequent simple steps.
These are the rules as I learned them way back when.

For 999km and then 9km:
sqrt(9^2 + 999^2) = 999.0405397km
9^2 = 81 but should only have 1 sigfig in the tens place.
999^2 = 998001 but should have 3 sigfigs with the last one in the thousands place.
998001 + 81 = 998082 but since the 998001 is only known to the thousands place it should only have 3 sigfigs.
sqrt(998082) = 999.0405397 but should be rounded off to 3 sigfigs for the final answer.
The final answer according to the rules is 999km.

For 999km and then 99km
sqrt(99^2 + 999^2) = 1003.893421km
99^2 = 9801 but should only have 2 sigfigs with the last one in the hundreds place.
999^2 = 998001 but should have 3 sigfigs with the last one in the thousands place.
998001 + 9801 = 1007802 but only has sigfigs to the thousands place leaving a number with 4 sigfigs this time.
sqrt(1007802) = 1003.893421 but should be rounded off to 4 sigfigs in the final answer.
The final answer according to the rules is 1004km.

For 999km and 999km
sqrt(999^2 + 999^2) = 1412.799439km
999^2 = 998001 but should have 3 sigfigs with the last one in the thousands place.
998001 + 998001 = 1996002. It should have its last sigfig in the thousands place leaving 4 sigfigs.
sqrt(1996002) = 1412.799439km but it should be rounded off to 4 sigfigs in the final answer.
The final answer according to the rules is 1413km.

Please note that I'm not trying to get in an argument here of whether doing all that work is worth it or important. I'm just laying out what the correct answers are according to the rules.

Note the closing paragraph. I wouldn't put it better.

 

[tiny-tim]

That's nice!

Borek, is JB a PF member? If so, would he like to do a Library article on significant figures ?

(We do keep getting questions on it.)

(btw, I've just checked, and "significant figures" gets a lot more hits on a forum search than "sig figs" … 500 in 30 months as opposed to 471 total)

 

[ThomasMagnus]

Thank you very much for the help!

I e-mailed my instructor on this and he said: "I don’t worry about significant digits, and I suggest you don’t either. As long as you follow the right procedure(s) and your final answer is correct within 2 decimal places, it will be acceptable to me."

Does this seem like what the normal response? Do sig figs really only matter in high school physics? For example on my sample final exams it says: Marks will not be deducted for expressing answers to 2 or 3 sig figs.

Thanks

 

[Borek]

Does this seem like what the normal response? Do sig figs really only matter in high school physics?

Yes².

 

[Upisoft]

What does it mean something specified in this way?:

4.13566733(10)

I guess it has something to do with precision.

 

[Borek]

4.13566733±0.00000010 - that is, number in parentheses describes accuracy of last digits.