HELP, please! Significant figures in Chemistry (again!)

[Hoggirl]

We are using Apologia Chemistry. We did four modules last year and have been reviewing those via the Red Wagon Tutorial CDs this year. We plan to use these lectures going forward. I had ds watch the eight lectures that cover the first four modules as review. I gave him the Red Wagon tests. He is getting some different answers, but he tells me it is because of when he is changing (w/n the problem) to the correct number of significant figures. So, WHEN does one take the problem to the correct number of significant figures? I thought one worked all the way through and then changed at the end, but he says Mr. Rosenoff sometimes changed to the proper number in the middle of the problem while sometimes he changed to the proper number at the end of the problem.

 

Arguing about this was a thorn in my side last year. I hoped having lectures would help, but apparently not. Is there a hard and fast RULE about when one converts to the proper number of significant figures?

 

BTW, science is the bane of my existence!

 

PS. How many significant figures are in:

 

34990 ml?

 

and how many are in:

 

3.500 x 10 ^ 4 ml?

Edited August 25, 2010 by Hoggirl

[Martha in GA]

the answer to your first question. I tend to work the whole problem and then figure sig. figs., but I noticed BJU also rounded off each answer before adding them when my ds was doing a heat related problem. I guess each part of the heat transfer only had a certain number of sig. figs. and then you would add them together, whereas, if you are multiplying numbers, you would keep all your sig. figs. to the end.

 

BUT, I DO know the answer to the second part of your question!

34490 ml as 4 significant figures

3.500 x 10^4 has 4 significant figures

[AngieW in Texas]

There are 4 sig figs in both of those numbers just as Martha said.

 

In general, it's best to carry 2-3 digits more than your final answer requires until the very end.

[Guest Cheryl in SoCal]

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

Edited August 25, 2010 by Cheryl in SoCal

[Mom22ns]

I agree, both numbers have 4 significant figures. I have ds round at the end. When there are numbers of significant extra length, he can round during the problem, but I always have him carry along one or more extra significant figures during intermediate steps.

[Hoggirl]

Cheryl, I do believe this will help. I have been trying to determine a hard and fast rule that, when consistently applied, will result in ds not having any rounding errors.

 

I appreciate everyone's input!

[Susan C.]

We are just starting Apologia Chemistry. I did it five years ago with my son. So I am going from long ago memory..

 

I remember ds answers were always close to the key. Sometimes a different number of decimal places, sometimes just close. I finally got to the point that if it was close, and if it was set up correctly, I would give it to him as correct. Fast forward to two years later with him, doing BJU Physics. The teacher did a very detailed lesson about how to do significant figures and it was the best explanation I have ever heard. But, at the end, he said for the rest of the school year that he wanted answers to three decimal places, and if the answers were in the ranges he gave on the keys, they would be correct. The answers get skewed if you round during the process, rather than just at the end.

 

So, I am going to relax with dd.

[ChemMommy]

I teach students to do problems that involve multiplication and division all the way to the end and then adjust sigfigs. You must stop and adjust sigfigs whenever you switch between addition/subtraction and multiplication/division. So, if you were adding two masses and then multiplying by some conversion factors, you would need to add the two masses, adjust the sigfig following the add/subtract rules. Then, you would need to do the multiplications and adjust the sigfigs according to the sigfig rules for multi/division.

 

The last digit listed in the final answer is the "digit of uncertainty". It is the ONE digit in the whole answer that can vary from the answer key without concern.

[yinne]

When we were doing chemistry last year, I found these links that helped us figure out signigicant digits. They might be of some help.

 

http://www.usca.edu/chemistry/genchem/sigfig2.htm

 

http://www.usca.edu/chemistry/genchem/sigfig.htm

 

http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm

 

http://www.chem.sc.edu/faculty/morgan/resources/sigfigs/sigfigs3.html

 

Yvonne in NE