Need someone to double check a simple problem with sig figs

[ksinelli]

I'm trying to get back into physics, and was brushing up on some very basic concepts. I came across this problem on a website tutorial.

"Solve -9.300 + 2.4 * 3.21"

It's a problem to practice rounding with significant figures. The instructions say to round to significant figures only when you reach a final answer.

So here's what I did.

2.4 * 3.21 = 7.704 (I left the three decimal places as the instructions say to only round at the end.)

-9.300 + 7.704 = -1.596

So I came up with an answer of -1.596, since there are 3 significant figures after the decimal place in both numbers for the addition portion of the problem.

But the website says the answer is -1.6

I don't understand why they rounded to two sig figs. Is this an error on the website, or am I not understanding something?

This is the website for anyone who wants to check it out. The problem is about midway down the page.

http://library.thinkquest.org/10796/ch1/ch1.htm

 

[LowlyPion]

I'm trying to get back into physics, and was brushing up on some very basic concepts. I came across this problem on a website tutorial.

"Solve -9.300 + 2.4 * 3.21"

It's a problem to practice rounding with significant figures. The instructions say to round to significant figures only when you reach a final answer.

So here's what I did.

2.4 * 3.21 = 7.704 (I left the three decimal places as the instructions say to only round at the end.)

-9.300 + 7.704 = -1.596

So I came up with an answer of -1.596, since there are 3 significant figures after the decimal place in both numbers for the addition portion of the problem.

But the website says the answer is -1.6

I don't understand why they rounded to two sig figs. Is this an error on the website, or am I not understanding something?

This is the website for anyone who wants to check it out. The problem is about midway down the page.

http://library.thinkquest.org/10796/ch1/ch1.htm

I believe that the rule is to round to the number with the least precision of the numbers you used to calculate it with.

In your case that would be the 2.4 number. Which implies the answer should be of the form xxx.x, so they expect you to round 1.596 to 1.6.

 

[ksinelli]

Hm, ok. I think I understand what you're saying. You're saying that if you have a problem with multiplication and addition, you use the rule for rounding addition problems, but you include *all* the numbers in the problem, not just the numbers that were added?

If that's the case though, then what about this sample problem that is given..

3.6 * 0.3 + 2.1 = 1.08 + 2.1 = 3.18 = 3.2.

Wouldn't the answer just be 3 then, as 0.3 only has one significant figure?

 

[LowlyPion]

Hm, ok. I think I understand what you're saying. You're saying that if you have a problem with multiplication and addition, you use the rule for rounding addition problems, but you include *all* the numbers in the problem, not just the numbers that were added?

If that's the case though, then what about this sample problem that is given..

3.6 * 0.3 + 2.1 = 1.08 + 2.1 = 3.18 = 3.2.

Wouldn't the answer just be 3 then, as 0.3 only has one significant figure?

If the statement of the problem had been 3.6 * .3 + 2 = ...
then the 2 with no decimal point would have suggested rounding to 3.

But with the least precision number showing 1 place after the decimal that's where I think you want to end up.

 

[LowlyPion]

Arithmetic

For multiplication and division, the result should have as many significant figures as the measured number with the smallest number of significant figures.

For addition and subtraction, the result should have as many decimal places as the measured number with the smallest number of decimal places.

http://en.wikipedia.org/wiki/Significant_figures

 

[ksinelli]

Oh ok. I understand now. In my second post I was going back to using the rule for rounding with multiplication and division problems, instead of the rule for addition and subtraction like you said. Silly me =/

Thank you much for the clarification :)