This screencast is going to be about significant figures, or "sig figs", as we call them. And
the first thing is how to describe them--how many do you have?
The definition is the digits from the 1st non-zero digit, that is to the left, and
then from there, you go either to the last digit on the right if there's a decimal point
or if there isn't a decimal point, so we have no decimal point, then it's the last non-zero digit of the number.
So, let's take a look at some examples. Let's say we have 4500--no decimal point, so from
the first non-zero to the left to the last non-zero since there's no decimal point. And
that would mean we have 2 sig figs.
However, if we put a decimal point here, now we have to count all four of those numbers,
so that's 4 significant figures.
Now we write it like this: 0.045. So here, we have 2 significant figures. However, if
we put a zero after that five, now that zero becomes a significant figure.
So let's say we want to write this in scientific notation. This would be 4.5 x 10^3. However,
this would be 4.500 x 10^3. This would be 4.5 x 10^(-2), but this one would be
4.50 x 10^(-2).
So look at the difference that not only a decimal point makes, but also a zero following
the last digit after a decimal point.
So now that you know how many significant figures there are.
What happens if we want to multiply or divide two or more numbers? How many significant
figures do we report in the answer? What we do is we report the lowest number of significant
figures in any of the numbers we're multiplying or dividing.
And this does not include converging factors. So for example, if we multiply 4.3 times 5.27, in
our calculator, we get 22.661, but that's not what we report because this has 2 significant
figures, this has 3 significant figures. The lowest number of significant figures is two,
so this ends up being twenty-three.
Now, let's look at it in terms of dividing. So we take 6.89 we divide it by 1.357, and
in our calculator, we get 5.07737, et cetera. However, this has 3 significant figures, this
has 4. The lowest number of significant figures we have is 3, so this is 5.08.
Now let's look at addition or subtraction. This has to do with the position of the last
significant figure relative to the decimal point, so we report the one that's furthest to
the left, after the decimal point. Let's take a look at something like "83 - 4.67" and our
calculator gives us 78.33. However, if you look at this number, to the right of the decimal
point, we have zero significant figures, even though this has two. So, we can have no figures
to the right of the decimal point, so we report this as 78.
Finally, let's do a combination. We have 1.03 and we add to it 4.734 and we subtract from
it 0.2, and we're left with 5.564. This has two figures after the decimal point, this
has three, but this has only one. So we have to report it as 5.6.