Tricky Chemistry Problem: Adding Sig Figs with Base Ten

[eriray]

Homework Statement

This is a chem problem for adding sig figs with base ten. The problem is: 3.15x10^-4 + 6.99x10^1 + 5 all divided by 7.73x10^-4. I was trying to help my daughter with this.

Homework Equations

The Attempt at a Solution

I can do sig figs pretty well and these kinds of problems. The answer I got was 9.69x10^4. My daughter tells me this is wrong and the answer is: 9.04x10^1 + 8! I've never seen an answer for these kinds of problems written out like this - so what am I missing and how the heck did they come up with this?
thanks for the help.

 

[Borek]

6.99
0.000315

obviously adding second number is irrelevant to the sum value.

But either I don't understand your notation, or something is simply wrong. 6.99+5 gives about 12, divided by 7.73*10^-4 gives something like 15500 (I am talking about ball park, not sig figs nor exact result) - which doesn't fit neither your answer nor your daugther's.

Are +5 and +8 parts of the sum, or is it something completely diferent?

 

[eriray]

My daughter read the problem to me via IM and a webcam (she's at OSU) so I didn't see how it was written out (it was on her computer) but showed her how I wrote it out and she said that was the way it was written. So, my assumption was it went like this: (3.5x10^-4 + 6.99x10^1 + 5)/7.73x10^-4. For ease of calculation, and because the base 10 exponents were small, I converted all to: (.000315 + 69.9 + 5)/.000773 = 74.900315/.000773 = 96895.62 = 9.69x10^4! However, she said the answer, according to the computer where she gets the questions and puts in the answers (for her chemistry class), was 9.04x10^1 + 8! So where does that +8 come from or did I somehow assume wrong in writing the problem out and therefor got the order of operations wrong? To me it seems like maybe you might be solving it as:
(3.5x10^-4/7.73x10^-4) + (6.99x10^1/7.73x10^-4) + (5/7.73x10^-4)? Which, according to the calculator, still gives an answer of 96895.67 or in sci. notation = 9.69x10^4! I don't see any other way to do it unless they way is was written out is different than what was given to me (like she forgot to mention some parenthesis set...etc...)
Thanks for your help,

 

[Borek]

I am an idiot, 69.9 it is

No idea what the 8 does mean, but if it is 69.9+0.000315+5 final answer should have IMO 2 significant digits (69.9+5 being 75). However - don't pay too much attention to that. Significant digits are faulty by desing and in reality (almost) never used - that is, she may lose some points writing things like 1.2345678976534 as an answer, but in most cases just using the same amount of digits in the final answer as the lowest accuracy input data will be enough.

Whenever it is important to really state accuracy of the result, no one uses significant digits, there are statistical methods designed especially for that purpose.

 

[eriray]

LOL! Yeah - I don't worry so much about the sig figs - just put the answer in the same number of sig figs as the lowest number in original problem (which all have 3 sig figs). So, the big question is where does that darn ...+8 come from? I'm really scratching my head over that! The basic rule for addition/subtraction of numbers in sci. notation, if my recall is correct, is the base (10) and exponents need to be the same (i.e. to add 3.45x10^3 + 1.28x10^2 one needs to make both exponents on the base 10 the same so you end up with... 3.45x10^3 + .128x10^3 OR 34.5x10^2 + 1.28x10^2 which would equal 35.78x10^2 both ways...or put in correct sig figs... 3.58x10^3). Obviously this doesn't need to be done if using a calculator because one just needs to plug and chug - but if doing by hand...then it makes it feasible to calculate - unless you are a brainiac! Maybe they teach this stuff differently these days...changed the rules and all...?lol.

opps - realize that maybe the number of sig figs is actually 1 because of that 5? Heck, I don't know...that would mean the answer would be something like 1x10^5 because 9.69x10^4 (which was the answer I got for the original problem) would be rounded to 10x10^4 and to 1 sig fig would be 1x10^5?? OMG this is getting complicated and still...WHERE DOES THE +8 COME FROM?LOL

 

[Borek]

No, it is not 1 sig fig. When it comes to addition and substraction rules are slightly different - 1234.1-0.001 has still 5 sig figs, as it depends on the position of decimal point.

I guess this 8 is something completely different, unrelated and only accidentally displayed in the same place

 

[eriray]

thanks for clearing up sig figs with addition - I forget all the rules! No matter - what really gets me is that +8! So, I will get to the bottom of this :) - I think my daughter gave the problem to me wrong...or ... maybe I just don't know what I think I know. Anyhow, if I clear it up I will be sure to post what the issue was! Thanks again for your help!