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Chemistry Forums for Students => High School Chemistry Forum => Topic started by: big on November 28, 2010, 02:02:30 PM

Title: How many significant figures?
Post by: big on November 28, 2010, 02:02:30 PM
How many significant figures should be reported in the answer to the calculation (Assume all numbes are experimentally determined):

(12.501*3.52/0.0042)+6.044?

So using 2 sig figs for just the multiplying and dividing, I got that it will become: 1.0*105+6.044 = 10006. However, am I supposed to use 5 sig figs or 2 sig figs then for this type of addition?
Title: Re: How many significant figures?
Post by: rabolisk on November 29, 2010, 08:51:33 AM
It should be 2.
Title: Re: How many significant figures?
Post by: Borek on November 29, 2010, 05:05:50 PM
Quote from: big on November 28, 2010, 02:02:30 PM
I got that it will become: 1.0*105+6.044 = 10006

That's incorrect, you should not round down before adding. Calculate using full accuracy available, round down at the end. It happens in this case it won't change the final result, but that's the common source of errors.
Title: Re: How many significant figures?
Post by: big on February 15, 2011, 06:34:11 PM
Quote from: rabolisk on November 29, 2010, 08:51:33 AM
It should be 2.

Can you explain that please? I'm not seeing why it's 2 if there's an addition sign in there.
Title: Re: How many significant figures?
Post by: opti384 on February 15, 2011, 10:34:06 PM
I also think that the final number of sig figs will not be 2.
Title: Re: How many significant figures?
Post by: rabolisk on February 16, 2011, 12:18:34 AM
It is 2. Let's say that you know that the population of a city is 150000. However, only the first 2 digits are accurate. You know for a fact that it is between 145000 and 155000, but you can only report it to 150000 with certainty. Now imagine that 100 extra people move into your city. Will you now say that your population is 150100, or still 150000?
Title: Re: How many significant figures?
Post by: opti384 on February 16, 2011, 12:27:24 AM
Yes 2 sig figs will be for this part 12.501*3.52/0.0042.

However, after you add you don't get the least sig fig number for your result like in dividing or multiplying.
Title: Re: How many significant figures?
Post by: rabolisk on February 16, 2011, 12:39:17 PM
The rule for addition is different from the rule for multiplication

http://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html

The first doubtful digit in 1.0 * 105 is the 0. 6.044 makes no difference because all of those digits are to the right of the 0 of 1.0 * 105. Again it only makes sense that if you have 150000, but you can only say for certain that it is somewhere between 145000 and 155000, then adding 6 does not change what you report.