While determining the correct number of digits to include is a straightforward process, beginning students often overlook this important detail. Here we outline the rules involved in determining the appropriate number of digits to include when reporting results of calculations and experimental measurements.
Skills: Reporting scientific results with the appropriate number of significant digits. By using significant figures, we can show how precise a number is. If we express a number beyond the place to which we have actually measured and are therefore certain of , we compromise the integrity of what this number is representing.
It is important after learning and understanding significant figures to use them properly throughout your scientific career.
So you have carried out a calculation that requires a series of seven or eight mathematical operations and at the end, after punching everything into your calculator, you see the result " Intro to significant figures. Rules of significant figures. Multiplying and dividing with significant figures. Addition and subtraction with significant figures. Practice: Significant figures. Current timeTotal duration Google Classroom Facebook Twitter.
Video transcript Based on the examples in the last video, let's see if we can come up with some rules of thumb for figuring out how many significant figures or how many significant digits there are in a number or a measurement. So the first thing that is pretty obvious is that any non-zero digit and any of the zero digits in between are significant. Clearly, the 7 and the 5 here are significant. And the 0 in between them, it's also going to be significant.
So let's write this over here. So any non-zero digits and zeros in between are going to be significant. That's pretty straightforward. Now, the zeros that are not in between nonzero digits, these become a little bit more confusing. So let's just make sure we can rule out some of them. So you can always rule out when you're thinking about significant figures, the leading 0's.
And when I'm talking about leading zeros, I'm talking about the zeros that come before your non-zero digit. So these are leading zeroes here.
These are leading zeroes. There is no leading zeroes here. No leading zeroes in this one, this one, and this one. But in any situation, the leading zeros are not significant. So leading zeros not significant, I'll write it over here. Leading zeros not significant. And so the last question, all you have left, I mean you only have non-zero digits and zeros in between. You could have some leading zeros, which you've already said are not significant.
And so the only thing left that you have to figure out is what do you do with the trailing zeroes, the zeroes behind the last non-zero, or to the right of the last non-zero digit. So these trailing zeroes here. There's actually two trailing zeroes over here. And then there's three trailing zeroes over here. So let me make a little-- so trailing zeroes.
Trailing zeroes, what do we do with them? So the easy way to think about is if you have a decimal, if there's a decimal anywhere in your number, count them. If you have a decimal, count them. Count them as significant. They are significant, count them as significant. If there's no decimal anywhere in the number, then it's kind of ambiguous. You're kind of not sure and this is a situation.
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