Anonymous

# What is a significant figure?

Can someone please give me a dumbed-down definition of significant figures and then maybe a few exampless. thankss :)

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• Anonymous

Significant figures are a way for us to deal with the precision of measurements and numbers.

Lets say you're driving on the highway, and you see a sign that your destination is 300 miles away. Now lets say you're driving a car with a really nice speedometer that tells you you're going exactly 70.5 miles per hour. Simple math tells you it'll take you 300 / 70.5 = 4325531914 ... hours to get there.

But isn't that kind of ridiculous? It's going to take you 4.25531914 hours and not 4.25531915?

Of course, because that sign that said 300 miles isn't perfect. It might be 300.5 or 299.1 miles or even 290 miles. It could've been rounded from anywhere from between 250 and 349 miles to 300 miles.

So based on the rules of significant figures, we say that 300 miles only has one significant figure. That means whatever answers we get based on using that 300 miles can only have one significant figure too (for multiplication and division, slightly different for addition and subtraction). So our time becomes to travel becomes somewhere around 4 hours, because that's the best we can say based on our really bad measurement of 300 miles.

Suppose we have GPS in the car too though. And it says its 305 miles to our destination. Well now we know that couldn't have been rounded from more than 304.5 to 305.49 miles. Accordingly, we can say now that our trip will be 305 / 70.5 = 4.32624 ... hours, which we could keep 3 significant figures from: 4.33 hours.

All this does is let us know how carefully something was measured and then make sure that we don't tell someone else was much more carefully measured than it actually was (usually because that's just what our calculator spit out)

• Anonymous

Aha I just learned this today :D

my teacher explained that significant figures is like counting money. the more detailed, the more possibility that it is a significant figure.

examples of numbers that has significant figures (sf)

a.) 90.00 - since this number is followed by two decimals, all numbers count as significant figures. so the number of sf in that is 4. there are four significant figures in there

b.) 2072 - this number has captive zeros, which means that there are zeros in the middle of other numbers, but it does not have any decimals. the analogy of counting money makes this easier. imagine if someone just counted 2000. this number basically gives you more detail, until you know the ones and the tens. so all numbers count as sig-figs in here. there are 4 sig figs.

c.) 0.0004 - zeroes that are not captive does not count as sig-figs. so the only sig-fig here is 4. there's only one sig-fig.

MORE CAPTIVE ZEROES examples

909

12134810000007

6003.56

0.500000012

Source(s): chemistry class - sorry i cudnt be more specific. hope this helps a little bit