Now that we've learned the rules about how to tell whether 0 is significant or not, let's
take a look at calculations involving numbers with 0’s in it.
We’ll go through this really quickly.
I got a couple of multiplication and division problems here, let's go through them.
307 here has three significant figures because of this sandwiched 0 and 32,000 has two significant
figures because 0’s that are coming to the right of significant figures when the number
doesn't have a decimal point are not considered significant, right?
So that means that when we multiply these together here's the answer that we get that
our calculator spits out we want to round it to two significant figures so we’ll keep
the 9, we’ll keep the 8, we’ll look next door to the 8 whether to round up or down,
we keep it the same.
So we keep the 9, we keep the 8 and we fill everything else in with 0’s.
Alright so now that you've learned that significant…
or now that you've learned that 0’s to the right of non-zero digits are not significant
now you understand why filling in the rest of the number with zeros leaves you an answer
that has only two significant figures, the 9 and the 8 and nothing more.
Alright let's look at this one here.
Four significant figures here because zeros to the right of a non-zero number are significant
when there’s a decimal place in the number and this is easy… three significant figures
here because there are no 0’s here they're all non-zero digits, always significant.
Which means that we're going to round this to the lower of them to 3 so we're going to
go one, two, keep this and look to the right to see whether we should round it up or round
it down.
It’s a 0 so we keep it the same.
So we're going to turn this in to 0.0, neither of those are significant because they're to
the left, 150 and 0 is significant because it’s to the right of non-zero numbers and
there's just one decimal place the number so that is our final answer there.
When we divide these guys, here is the ugly answer that our calculator spits out, how
do we round it?
Well, there are five significant figures here because there are 0’s to the right but there's
a decimal point, there are only two significant figures here because there are zeros to the
right but there is no decimal place which means that we take the lower of them, 2, and
we’re going to round this number to two significant figures.
These guys to the left are not significant so we don't have to worry about them.
We're going to keep the 2 and we're going to keep the 0 and look next door to see whether
we should round up or keep it the same.
We're going to round up because it’s an 8 so we're going to get 0.0 to the left, so
they're not significant, 21 and that there is our final answer.
Let's do two more here.
0.0005 only one significant digit there because we can ignore all the 0’s to the left of
a non-zero number.
One there and one-two-three here, ignoring this one to the right because there is no
decimal place there, so three significant digits there.
That means that we're going to round our answer to only one significant digit.
0 we don't have to worry about because it's not significant.
We're going to keep the four and we're going to look next door to see whether we should
round up or down, we will round it up 0.5 is our final answer.
And finally, these guys multiplied together 0.0 we don't worry about those 301 the 0 is
sandwiched in between these guys so it’s significant and the 0 to the right is also
significant because there's a decimal place in the answer.
Four significant figures here, 503, we know those are significant because of the sandwich.
Now the idea here is the 0 to the right, is it significant or not?
It's not because there is not a decimal place in the number which means we're going to be
rounding our answer here to only three significant figures.
The 1 stays, the 5 stays and 1 stays, we look next door to keep it the same or round up,
it is a 4 so we keep it the same.
So our final answer is 151.