let's talk about sigfig rules. Of course
sigfig stands for significant figures
and I think it's fair to say that sig
figs are one of the most hated concepts
by chemistry students yet they're one of
the most important they're in almost
every single problem you end up doing
and so it's really important to hammer
in those rules just as additional notes
sometimes you'll see them written as s
FS if you've ever stood on a piece of
paper or exam grade with points off that
stands for sig figs okay so today I'm
going to go over the five rules that
kind of guide all the sig figs and this
is all you need to know to assign how
many sig figs are in any number so
starting with rule number one any
nonzero numbers are sig figs so this
takes care of most of your numbers right
one through nine anytime you see
anything that's not a zero that is a sig
fig so now let's do a couple of examples
just to drill that so seventeen are two
digits are one and seven neither of
those are zeros which means both of them
are sig figs and so our total number of
sig figs in this number is two and that
goes for five thousand six hundred and
thirty one point five four doesn't
matter if it's a decimal point or a big
number as long as it's not a zero that's
always going to be a sig fig so in this
case our five or six or three our one
our second five and our four are all sig
figs so the total number of sig figs in
this number is six all right
and so since we already took care of all
the nonzero numbers with rule number one
rules to three for a and for B are just
talking about zeros so when we talk
about sig fig rules and how to assign
sig figs we're really talking about
zeros those are the hard ones
so rule two any zeros in between two non
zeros our sig figs okay so let's go over
to an example we have the number 101
right away we know that both ones are
definitely going to be sig figs just
because they're not zero so we can check
those off and then now our zero is in
which
mean to non-zeros it's right in between
those two ones so it is going to count
as a sigfig so this means that our
number 101 has a total of 3 sig figs and
that goes for the next example as well 2
million and 9 and so you we know that 2
& 9 are both going to be sig figs
because they're not zeros and you can
take a look at all of these zeros all 5
of them are going to be sig figs because
eventually you might have to go out a
couple of zeros for the one in the
middle but eventually you would get to
some non zero for every single one of
those zeros on both ends so it doesn't
matter even though the zero in the
middle still has a bunch of zeros around
it eventually it is in between two non
zeros so it's always going to be a sig
fig and this is also called like a
middle zero those are always going to be
sig figs so we can check everything on
this number and the total number of sig
figs that this number has is seven all
right so now moving to rule number three
any zeros before non zeros are not sig
figs so this is we basically just going
through all the different types of zeros
we can have so we've already dealt with
them in the middle and now we're talking
about zeros that happen before non zeros
non zeros are just numbers one through
nine so for this example let's look at
point five we can see there's that zero
there on the five the five we know is a
sig fig so it's not a zero so we can
check that off and now we look at where
that zero is and it's not in the middle
so it doesn't count it's before so it
definitely doesn't count so it doesn't
this doesn't matter for any doesn't
matter what place you're in it's not
going to count if you're before the
numbers and so 0.5 is just going to have
one sig fig and then if we look down at
our next example its point zero zero
zero one 305 so in this case we can
immediately check off all of our non
zeros we know one three and five are all
going to be sig figs and now that one Oh
in between the three and the five that's
rule - that's a middle zero so that
counts and now Rule three that's talking
about every single zero that we see
before you see that
first nonzero one so these one two three
four zeros are all not sig figs because
they're before and so the total number
of sig figs this number has is four it's
the last four digits you see all right
so now let's go to rule for a this says
that any zeros after non zeros in a
number without a decimal point are not
sig figs and so rule for a and rule for
B are just talking about zeros that
happen after the numbers because in two
we took care of the middle in three we
took care of the ones that come before
for a and for B are just two zeros that
are after all of your non zeros so for a
is just talking about numbers without a
decimal point whether or not even
whether or not you have a decimal point
really matters for sig figs
so if we look at 500 we know that five
is going to be a sig fig because it's
not a zero and then both of our zeros
are after that five so they're called
trailing zeros sometimes and because
there's no decimal point in that entire
number they're both not sig figs we
don't count for anything so the entire
number of sig figs in the number 500 as
written is only one and that goes for
the same thing as 10,000 so there is no
decimal point in that number and every
single zero you see comes after the non
zeros so that means that one of course
is a sig fig and then the four zeros
after it or not so again this for this
number the total number of sig figs with
entire number is just one so now let's
look at our last rule rule for B which
says any zeros after non zeros and a
number with a decimal point our sig figs
and so for a and for B we're just
talking about trailing zeros that happen
after all the numbers and we're just
talking about whether on the decimal
point so the rule is that if there is a
decimal point in any place and then
higher number everything with the
trailing zero every zero after the non
zeros is a sig fig so now let's take a
look at 500 the same number that we saw
a couple of examples ago but it's
written differently now this time it has
a decimal point in an extra zero so of
course five is going to be a sig fig so
that the non zero
now this time every single zero councils
a sigfig because there is that decimal
point there and so this 500 has a total
of 4 sig figs overall and so now let's
do a couple of combined problems so our
second-to-last we have Oh point zero
three 100 so none of our leading zeros
ever ever ever count that's not rule
number three and then we have three and
one
those are nonzero numbers they're always
going to count and now we have one last
zero it's a trailing zero it's after all
the non zeros and there is a decimal
point somewhere in the number which
means that it is going to count as a sig
fig so this number has three sig figs
and now let's do a really long example
that has a ton of different types of
zeros and other numbers so first I
always go around and I just check the
non zeros because those are the easiest
rule to follow it's not a zero it is a
sig fig so I check off one three nine
five and my other three and now I go
through and I check all my middle zeros
the kind of zeroes that are like this
meat of the sandwich in the number so
I've got three middle zeros I can check
off and so now I'm just looking at the
before zeroes and the after zeroes so my
trailing zero it's at the very end of
this number there's just one and even
though it's a bunch of decimal points
forward that decimal point is in the
number so this trailing zero does count
as a sig fagged and then all I have left
over are my two leading zeros which
happen before you see any non zeros
which means there's no way there sig
figs so both of these guys are not sig
figs and so in total this number has a
nine sig fig so it's first two don't
count alright well thanks so much for
watching that's all I have for you today
and good luck with sig figs I know
everybody hates them but they are really
important and they are useful okay
