Significant figures: a problem. After going all through web and posts I can't get a complete idea of significant figures. I'll try to explain the problem. The definition that seems more frequent is: > significant figures: number of figures carrying on precision. It is easy to see that in the number $1000$ zeros are non-significant figures unless we specify it as $1000.$. It is also clear that $0010.$ is two significant figures. Here it comes when definition shows unuseful (at least to me), because leading zeros as well as non zero numbers talk about precision. For example $0.0017$ and $0.1217$ are same precision. They indicate the measuring instrument can detect variations in the ten-thousands. If not, please explain how. That's the specific problem. I beg you answer with _concrete_ examples. * * * The most interesting site I've read is this , and I understand how significant figures work, but the previous problem remains.

I've understood it by this way:

Suppose we have sand grains of $0.0005$ grams each one, weighed with a 0.0001 precision balance. Of course, the numbers before $5$ have a meaning: they indicate _magnitude_. But they are not significant figures. It can be seen in this way:

somebody estimate grains' number in $63566$. If we want to estimate the total weight, we should multiply. But there is 'no difference' between $0.0005$ and $0.0006$. Let's see how it modifies the multiplication:

$ 0.0005\times 63566=31783$

$ 0.0006\times 63566=38396$

So we can't even trust the first number, as if only the five $0.0005$ were meaningful. We can see it easily if we write it as $5\times 10^{-4}$

Once understood, $31783$ should be written as $3\times 10^{4}$