Question on Significant Digits

[jeri]

DD is doing Apologia Chem and although I *think* we have this down, sometimes I'm not so sure! Basically, when doing a two or more step problem (e.g. solve for something, then take that and solve for something else), do you deal with sig fig at all steps, or do you only deal with them at the end and use the fewest sig fig of any number throughout? Also, when dealing with "canned" numbers (such as 32 deg F or 1000g = 1 kg), I guess you don't include these in finding sig dig, right? Thanks.

 

Jeri

[emubird]

"Canned" numbers are assumed to be exact so you don't worry about them in sig digits.

 

I don't round anything until the final answer, and that seems to be what the textbooks I have are doing, based on their answers. If they were rounding in between, they'd come up with vastly different answers.

 

What I don't like about sig figures is that there seem to be 2 methods:

1) only report the number of figures that are sig

or 2) only report the same number of digits past the decimal point that the original data had.

 

I don't think 2 is really correct, but I keep running into chem books that do this (even after only explaining method 1). Method 2 really shouldn't be correct, in my thinking, because it won't work if you put data into scientific notation.

 

Has anyone else found this discrepancy?

[shea]

Jeri,

We were having problems with the significant figures also. I did a search, and I found the link below to be the most helpful. It is a tutorial on the significant figures and even has some practice problems to help with reinforcement. HTH.

Sue

 

http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/index.html

[Guest Cheryl in SoCal]

"Canned" numbers are assumed to be exact so you don't worry about them in sig digits.

 

I don't round anything until the final answer, and that seems to be what the textbooks I have are doing, based on their answers. If they were rounding in between, they'd come up with vastly different answers.

 

What I don't like about sig figures is that there seem to be 2 methods:

1) only report the number of figures that are sig

or 2) only report the same number of digits past the decimal point that the original data had.

 

I don't think 2 is really correct, but I keep running into chem books that do this (even after only explaining method 1). Method 2 really shouldn't be correct, in my thinking, because it won't work if you put data into scientific notation.

 

 

Has anyone else found this discrepancy?

Method 1 is for when you are multiplying or dividing. Method 2 is for when you are adding or subtracting.

 

ETA that you will need to round and figure significant digits when you switch from multiplying/dividing to adding/subtracting, and visa-versa.

Edited October 14, 2010 by Cheryl in SoCal

[Guest Cheryl in SoCal]

This is post I wrote from another thread and thought it might be helpful so I'm cutting/pasting it here.

 

The rules for addition/subtraction and multiplication/division are different. When you are adding/subtracting you are dealing with precision and would round your answer so that it has the same precision as the LEAST precise measurement in the equation (25.13 - 22.0 = 3.1 because the least precise measurement goes to the tenths place). When you are multiplying/dividing measurements you round the answer so it has the same number of significant figures as the measurement with the LEAST amount of significant figures (25.13 x 22.0 = 553 because the number with the least amount of significant figures has 3 significant figures).

 

I believe Apologia had us checking significant figures after each step.

 

ETA that by step I'm referring to when you need to use more than one formula to figure out the answer.

 

For example:

 

q = m x c x delta T

 

delta T = T final - T initial

 

If you needed to calculate delta T to use in the first formula you would convert the answer to the correct significant figures before plugging it into the first formula. You would also do this because it's the end of your addition/subtraction and would then be multiplying/dividing the answer, and the answer not being converted into significant figures would affect the final answer).

 

However, in the following problem you would do all the multiplication/division from left to right and then convert to correct number of significant figures. You would multiply 5.0 x 1.95 x 2.2 and then convert to the correct number of significant figures. You wouldn't multiply 5.0 x 1.95 and convert that answer to the correct number of significant figures and multiply that answer by 2.2. Does that make sense?

 

q = 5.0 g x xxxx1.95 J x xxx2.2 degrees C

xxxxx1xxxxxg x degrees C xxxxxxx1

[regentrude]

Basically, when doing a two or more step problem (e.g. solve for something, then take that and solve for something else), do you deal with sig fig at all steps, or do you only deal with them at the end and use the fewest sig fig of any number throughout?

 

When you do multiple step problems, you need to carry all digits through your calculation and cut off to sig figs for the final result. Otherwise, your round-off errors can accumulate which will be a problem with longer calculations.

If intermediate results have to be stated, you can use sig figs, but carry all the digits if the number is used in further calculations.

And yes, the least accurate quantity, the one with the fewest sig figs, determines teh accuracy of the result.

[jeri]

The following problem would come out on the calculator to 21.45 J, but since the smallest number of significan digits is 2 (for both 5.0 and 2.2) then it would end up being only 21 J.

 

 

q = 5.0 g x xxxx1.95 J x xxx2.2 degrees C

xxxxx1xxxxxg x degrees C xxxxxxx1

 

 

Is that right? thanks.

 

Jeri

[jeri]

how did you get those little invisible x's in there to show spacing?

 

jeri

[Guest Cheryl in SoCal]

The following problem would come out on the calculator to 21.45 J, but since the smallest number of significan digits is 2 (for both 5.0 and 2.2) then it would end up being only 21 J.

 

 

q = 5.0 g x xxxx1.95 J x xxx2.2 degrees C

xxxxx1xxxxxg x degrees C xxxxxxx1

 

 

Is that right? thanks.

 

Jeri

Yes:001_smile:

[Guest Cheryl in SoCal]

how did you get those little invisible x's in there to show spacing?

 

jeri

I type them in so everything lines up then highlight them and change their text color to white.

[jeri]

But I'm disappointed that I only got 7 right :(

 

It was the exponents that had me totally messed up! I will have to go back and review that part.

 

Great find though!

 

Jeri

[Susan C.]

The following problem would come out on the calculator to 21.45 J, but since the smallest number of significan digits is 2 (for both 5.0 and 2.2) then it would end up being only 21 J.

 

 

 

 

Jeri

 

To get it right in dd's class, she would have had to write 2.1 x 10^1

[Guest Cheryl in SoCal]

To get it right in dd's class, she would have had to write 2.1 x 10^1

If the answer needed to be written in scientific notation. The problem I quoted did not.

 

ETA that occasionally an answer will need to be written in scientific notation because writing it in standard form will give it the wrong number of significant digits. For example, if the answer was 50 and you needed 2 significant digits then it would have to be written as 5.0 x 10^1 even if the answer didn't need to be written in scientific notation because 50 has only 1 significant digit.

Edited October 15, 2010 by Cheryl in SoCal

[jeri]

Again, thanks for the help!

 

Jeri

[Guest Cheryl in SoCal]

You're welcome! I noticed an error in my previous post and corrected it. I had written 5 x 10^1 power when it should have been 5.0 x 10^1 (the .0 being needed for the second significant digit). Funny how things in your head don't always make it through your fingers to the keyboard, LOL.