Download 3 PPT Significant figures and math handout

8/25/2016
Significant Figures
How to Determine # of Sig Figs And
Mathematical Calculations
Significant Figures
At the conclusion of our time
together, you should be able to:
1. Explain what significant figures are in a
measurement
2. Determine the number of significant figures
in any measurement
3. Round calculations to the correct number of
significant figures.
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Significant Figures – Page 23
The significant figures in a measurement include all
of the digits that are known, plus one last digit
that is estimated.
The numbers reported in a measurement are
limited by the measuring tool.
Page 23
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Easier Way to do Sig Figs!! – Page 25
Pacific/Atlantic

P
A
If a decimal point is present, start on the Pacific (P)
side and draw an arrow through the number
until you hit a non-zero digit. Count all
numbers without an arrow through them.
If a decimal is absent, start on the Atlantic (A) side
and draw an arrow through the number until
you hit a non-zero digit.
Examples:
123.003 grams
decimal present, start on “P” side, draw
arrow, count digits without an arrow
through it.
Answer = 6
10,100 centimeters
Decimal absent, start on “A” side, draw an
arrow, count digits without an arrow
through it.
Answer = 3
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Page 25
1.
2.
3.
4.
5.
6.
1.23 cm
5.0 cm
0.005 cm
8.000 cm
500 cm
0.0420 cm
Learning Check
In which set(s) do both numbers contain the
same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
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Learning Check
A. Which answer(s) contain 3 significant figures?
1) 0.4760
2) 0.00476
3) 4760
B. All the zeros are significant in
1) 0.00307
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Example Problems – Add to Page 26
In each calculation, round the answer to the
correct number of significant figures.
1. 235.05 m + 19.6 m + 2.1 m =
2.
58.925 m - 18.2 m
=
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Example Problems – Add to Page 26
1.
2.19 m X 4.2 m =
2.
4.311 m ÷ 0.07 m =
Rules for Rounding Off



If the digit to be removed
• is less than 5, the preceding digit stays
the same
• is equal to or greater than 5, the
preceding digit is increased by 1
In a series of calculations, carry the extra
digits to the final result and then round off
Don’t forget to add place-holding zeros if
necessary to keep value the same!!
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Significant Figures and Numbers
Some numbers are
exact: There are
60 seconds in 1
minute
25 cents in 1
quarter
There is no uncertainty
in any of these numbers.
12 eggs in one
dozen
In other words there are
12.0000000000000000000000000000000000
eggs in 1 dozen
(add as many zeros as you like)
Counting Numbers
 Counting
 Ex:
numbers have infinite sig figs.
3 apples
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Significant Figure Math Rules
Addition / Subtraction Problem:
Penny Example =
0.019 m using meter stick
0.0192 m using ruler
0.0191 m using calipers
0.019046 m using
micrometer
To find the total =
0.076346 m

But most of my measurements have fewer
decimal places than my best tool!!!
Significant Figure Math Rules

Addition / Subtraction:
Answers can’t have more numbers to
the right of the decimal point than the
number in the problem with the least
amount of numbers to the right of the
decimal point.
Example =
24.1 m + 3.35 m + 2.23 m
Calculator says: 29.68 m (wrong)
Answer:
29.7 m
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Adding and Subtracting
The answer has the same number of decimal
places as the measurement with the fewest
decimal places.
25.2 m
one decimal place
+ 1.34 m two decimal places
26.54 m
answer 26.5 m (one decimal place)
Significant Figure Math Rules

Multiplication / Division Problem:
14.1 cm
3.3 cm
4.23 cm2
42.3 cm2
46.53 cm2
What should my answer be??
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Significant Figure Math Rules

Multiplication / Division:
Your answer can’t have more sig figs than
the number in the problem with the least
amount of sig figs
Example = 60.56227892 cm x 35.25 cm
Calculator says: 2134.890832 cm2 (wrong)
Answer:
2135 cm2
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