# Homework Help: Sig figs in answer? How does this work?

1. Feb 17, 2010

### Bensky

1. The problem statement, all variables and given/known data
The calculation to be performed is: 84.037 * (956/13.2 - 179/28.5 + 892/16.4)

The correct answer is: 1.013 x 10^4 but I don't see why this is. I got 3 sig figs in my answer, not 4. I have a test tomorrow at 7 PM - help before then is highly appreciated. This is the only problem I can't figure out.

Thank you.

2. Relevant equations
N/A

3. The attempt at a solution
84.037 * (956/13.2 - 179/28.5 + 892/16.4)=
84.037 * (72.4 - 6.28 + 54.4)
= 1.01 x 10^4

2. Feb 17, 2010

### mgb_phys

There are 3sf in the data you are given so it would be correct to give 3sig fig in the answer

3. Feb 17, 2010

### Bensky

So you're saying the answer on the answerkey is wrong and I am correct?

4. Feb 17, 2010

### vociferous

Yeah, generally speaking when you have quotients and products of measured (not defined) quantities, you want to keep the number of significant figures equal to the least precise measurement.

For instance, if you had: 1.34 (units) / 3.234354 (units) * 3 (defined constant)

You want to keep three significant figures in your answer because that is the least precise measured quantity.

If you have something like a mathematical or defined constant (like, base 10 or 1000 g/kg) then that does not affect your significant digits.

5. Feb 17, 2010

### mgb_phys

Yes, I wouldn't mark somebody down for putting an extra digit (it's useful if you need to carry the calculation further) but you are correct.

6. Feb 17, 2010

### Bensky

This is a multiple choice test unfortunately :( -- to be clear the question is going to ask specifically about the number of sig figs in a calculation exactly like the above one but with different numbers.

Anyway, I think I found my error (this SHOULD be 4 sig figs after all I think):
84.037(72.4 - 6.28 + 54.4)
84.037(66.1 + 54.4) //since 6.28 has 2 numbers past the decimal place and 72.4 only has one, result must be adjusted to only 1 number past the decimal
=84.037(120.5) //120.5 has 4 sig figs while 84.037 has 5, so 4 sig figs must be used.

Can someone confirm my logic on my second step and my final result?

7. Feb 17, 2010

### Bohrok

That's correct; 72.4 - 6.28 + 54.4 is 120.5 with four sig figs. Sometimes when adding or subtracting, you end up with more sig figs than you started with. Once you multiply or divide, you go with the fewest number of sig figs you're working with.

8. Feb 17, 2010

### Bensky

Okay, great!

Thanks for the help all.