Significant Figures
Have your notebook out.
2.
Bring your Variables
Worksheet up to be stamped.
1.
Homework
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Sig Figs Worksheet 1, due
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Tonight, you will only be able to do
problems #1-2. Leave problem #3 alone;
you’ll be able to do it after tomorrow’s
lesson.
Variables Worksheet
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Group corrections
Significant Figures
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Notebooks out! Title this section of your
notes “Significant Figures.”
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Before you can begin collecting your
data, you need to know the
mathematical standards you’ll be held
to…
Significant Figures
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The big ideas:
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Scientists need to know how strong their
measurements are. We use “significant figures” to
show that strength.
The more significant figures a number has, the
stronger the measurement it was.
Using better measurement tools gives you
numbers with more sig figs.
There are rules for figuring out how many sig figs
there are.
Significant Figures

Say you want to measure this guy from
eartip to eartip.
QuickTime™ and a
decompressor
are needed to see this picture.
Significant Figures
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Say you want to measure this guy from
eartip to eartip.
QuickTime™ and a
decompressor
are needed to see this picture.
Significant Figures
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When you take a measurement, you
can estimate one extra digit beyond the
ones on the instrument, but no more
than one.
The better ruler gave us a more precise
measurement.
Significant Figures
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The Rules! When you figure out sig
figs, always follow these rules in this
order. Let’s practice on this number:
020,670.90
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1. All digits NOT zero are always
significant figures.
Significant Figures
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020,670.90
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2. Final zeroes after a decimal point are
significant.
3. A zero between two significant
numbers is significant.
4. All the zeroes that are left are NOT
significant.
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Sig Figs Practice
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How many sig figs?
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0.00416
Sig Figs Practice
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How many sig figs?
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0.00416
Rule 1: Underline all non-zeroes.
Rule 2: Underline all zeroes trailing at the
end after a decimal point.
Rule 3: Underline all zeroes in between
other underlined numbers.
Rule 4: Cross out anything that’s left.
Sig Figs Practice
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How many sig figs?
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0.00416
Rule 1: Underline all non-zeroes.
Rule 2: Underline all zeroes trailing at the end
after a decimal point.
Rule 3: Underline all zeroes in between other
underlined numbers.
Rule 4: Cross out anything that’s left.
THREE SIG FIGS.
Sig Figs Practice
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How many sig figs?
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0.00416 =
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5.18 =
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200 =
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200.0 =
Sig Figs Practice
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Mini-competition: A sticker to the pair that
gets the most right answers! You may use
your notes.
3.0800
0.000054
91,106
76,000,000,000,000
0.00305
0.0080
Sig Figs Practice
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Come up with 10 significant figures problems,
at least five must include rounding. You must
know the answers to them.
Write the problems on a fresh sheet of paper,
and an answer key on another piece of paper.
When you’re done, give your “sig fig quiz” to
another group to solve.
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Check their answers when they’re done.
MORE fun with sig figs!
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(Sticker chance) How many sig figs are
in each of these numbers?
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40.08
32.9000
928,301.1
500,000,000,000,000,000
Homework
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Sig Figs worksheet, due Friday for B
and Monday for F.
MORE fun with Sig Figs!
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What if somebody measured the area of an
aye-aye ear like this?
QuickTime™ and a
decompressor
are needed to see this picture.
MORE fun with Sig Figs!
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A chain is no stronger than its weakest link.
One bad measurement makes your whole
result bad.
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When you add, subtract, multiply, or divide,
you can never get more sig figs than the
WORST of the numbers that you used.
QuickTime™ and a
decompressor
are needed to see this picture.
MORE fun with Sig Figs!
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How many sig figs can each of these
answers have?
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20 x 673
MORE fun with Sig Figs!
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How many sig figs can each of these
answers have?
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20 x 673 = The answer must have 1 sig
fig, since that is the worst of the
numbers we started with.
MORE fun with Sig Figs!
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How many sig figs can each of these
answers have?
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20 x 673 = 1 sig fig
0.041 x 248,200
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MORE fun with Sig Figs!
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How many sig figs can each of these
answers have?
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20 x 673 =
0.041 x 248,200 =
3.0800 / 0.003 =
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Rounding Sig Figs
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What if the problem’s answer has too
many sig figs or places past the
decimal? You must round it.
Take 20 x 673. We said that the answer
must have just one sig fig. Here’s how
to get there.
Rounding Sig Figs
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1. Do the operation normally first.
What is 20 x 673?
Rounding Sig Figs
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1. Do the operation normally first.
20 x 673 = 13,460 .
2. Count off the number of sig figs that
you need, starting from the leftmost
significant digit.
Rounding Sig Figs
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1. Do the operation normally first.
20 x 673 = 13,460 .
2. Count off the number of sig figs that
you need, starting from the leftmost
significant digit.
3. The last digit that you count to must
be rounded, the rest that you counted
past will stay the same.
Rounding Sig Figs
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20 x 673 = 13,460, which becomes
10,000
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Try these problems:
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8.9 x 10.8 . First, what normal answer do
you get?
Rounding Sig Figs
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8.95 x 10.81 = 96.7495 Next, how many sig
figs do we have to get this number down to?
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Starting with the leftmost significant digit (the
9) count off the sig figs you want, going
towards the right. The number you land on is
the number to round.
Rounding off 96.7495, we get…
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Rounding Sig Figs
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How about adding and subtracting?
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4.87 + 927.3
Sig Figs Practice
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Try these problems:
30 / 81
90.4 - 0.08
27,483 + 94,780
2.33 x 6.085 x 2.2
Sig Figs Practice
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Like before, design a “quiz” for another
team.
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8 questions.
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Two questions, present a single number and
ask how many sig figs it has.
Six questions, use multiplication, addition, etc.
Precision and Accuracy
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Pick up the handout.
Homework
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Twisted Rulers Analysis, go as far as
you can until you hit another (with class)
question
Sig Figs
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What’s the point of caring about sig
figs?
Precision
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Precision = How exact your
measurement is.
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Significant figures measure precision. The
more significant figures you have, the more
precise your measurement.
Is this the same thing as being right?
Precision & Accuracy
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Accuracy = How correct your measurement
is.
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Different from precision, and not measured by
sig figs!
What do I mean by that? Twisted Rulers lab
will hopefully illustrate the idea!
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Twisted Rulers Lab
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Groups of two tables.
Share rulers amongst groups, use them in
any order, just be SURE you record data for
the right letter!
Two volume stations.
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Instructions are at the stations. Learn to read
instructions out loud to the group before
attempting the operation!
Graded for: correct sig figs (estimating past
digits on rulers, multiplication). Feel free to
check with me on your sig fig work.
Accuracy
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Accuracy = How correct your
measurement is.
Sig figs can’t tell you this. Instead, a
procedure called percent error can.
Precision & Accuracy
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The equation for percent error (write it):
(Observed Value) - (Expected Value)
_______________________________ x 100
(Expected Value)