Sig figs in answer? How does this work?

[Bensky]

Homework Statement

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.

Homework Equations

N/A

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

 

[mgb_phys]

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

 

[Bensky]

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

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

 

[vociferous]

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

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.

 

[mgb_phys]

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

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.

 

[Bensky]

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.

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?

 

[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.

 

[Bensky]

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.

Okay, great!

Thanks for the help all.