Transcript Significant Figures - Solon City Schools

Significant Figures
In Measurements
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
Significant Figures
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.
How many sig figs are there in a given
measurement?
Measurement and Significant Figures
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Every experimental
measurement has a degree
of uncertainty.
The volume, V, at right is
certain in the 10’s place,
10mL<V<20mL
The 1’s digit is also certain,
17mL<V<18mL
A best guess is needed for
the tenths place.

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To indicate the precision of a measurement,
the value recorded should use all the digits
known with certainty, plus one additional
estimated digit that usually is considered
uncertain by plus or minus 1.
No further insignificant digits should be
recorded.
The total number of digits used to express
such a measurement is called the number of
significant figures.
All but one of the significant figures are
known with certainty. The last significant
figure is only the best possible estimate.
Below are two measurements of the mass
of the same object. The same quantity is
being described at two different levels of
precision or certainty.
Does 1 = 2???
1. assume a = b
2. multiply by b
3. ab = b2
4. subtract a2
5. ab – a2 = b2 – a2
6. factor each
7. a(b – a) = (b + a)(b – a)
8. divide by (b – a)
9. a = 2a
10. divide by a
11. therefore: 1 = 2
An Easier Way to have 1 = 2
Reading a Meterstick
. l2. . . . I . . . . I3 . . . .I . . . . I4. .
First digit (known)
= 2
cm
2.?? cm
Second digit (known) = 0.7
2.7? cm
Third digit (estimated) between
0.03- 0.05
Length reported
2.74 cm
=
or
2.73 cm
or
2.75 cm
Known + Estimated Digits
In 2.74 cm…
• Known digits 2 and 7 are 100% certain
• The third digit 4 is estimated (uncertain)
• In the reported length, all three digits
(2.74 cm) are significant including the
estimated one
Learning Check
. l8. . . . I . . . . I9. . . . I . . . . I10. .
What is the length of the line?
1) 9.3 cm
2) 9.32 cm
3) 9.33 cm
How does your answer compare with your
neighbor’s answer? Why or why not?
cm
Zero as a Measured Number
. l3. . . . I . . . . I4 . . . . I . . . . I5. .
What is the length of the line?
First digit
Second digit
Last (estimated) digit is
5.?? cm
5.0? cm
5.00 cm
cm
Always estimate ONE place past the
smallest mark!
11.5 mL
So how many sig figs are there in a given
measurement?
52.8 mL
Beware of Identity Theft!!
How to Determine Significant Figures in a
Problem

Use the following rules:
Rule #1
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Every nonzero digit is significant
Examples:
24 = 2
3.56 = 3
7
=1
Rule #2 – Sandwiched 0’s
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Zeros between non-zeros are significant
Examples:
7003 = 4
40.9 = 3
Rule #3 – Leading 0’s
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Zeros appearing in front of non-zero digits are
not significant
 Act as placeholders
 Can’t be dropped, show magnitude
Examples:
0.00024 = 2
0.453
= 3
Rule #4 – Trailing 0’s with DP

Zeros at the end of a number and to the right of
a decimal point are significant.
Examples:
43.00 = 4
1.010 = 4
1.50 = 3
Rule #5 – Trailing 0’s without DP

Zeros at the end of a number and to the left of a
decimal point aren’t significant
Examples:
300
= 1
27,300 = 3
Interesting Answers to Catholic
Elementary School Bible Questions:
Many religions teach that you are to
have only one wife
This is called Monotony.
Easier Way to do Sig Figs!!

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
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
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
Significant Figures and Numbers
60 seconds in 1
minute
25 cents in 1
quarter
Some numbers are
exact: There are
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
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Counting numbers have infinite sig figs.
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Ex: 3 apples

= 3.000 000 000 000 … apples
Significant Figures
Lets’ see if you can:
1. Explain what significant figures are in a
measurement
2. Determine the number of significant figures
in any measurement
Learning Check
State the number of significant figures in each
of the following:
A. 0.030 m
1
2
3
B. 4.050 L
2
3
4
C. 0.0008 g
1
2
4
D. 3.00 m
1
2
3
E. 2,080,000 bees
3
5
7
Significant Figures
And Mathematical Calculations
Significant Figures
At the conclusion of our time
together, you should be able to:
1. Determine the number of significant figures
needed for an answer involving
calculations.
2. Round math problems properly
Rules for Rounding Off
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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!!
13
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
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But most of my measurements have fewer
decimal places than my best tool!!!
Significant Figure Math Rules
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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
Another Example of 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
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Let’s Try a Multiplication / Division
Problem: Find the volume?
0.041m high
0.091 m wide
0.034 m deep
0.0001269 m3
What should my answer be??
Significant Figure Math Rules
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Multiplication / Division Problem:
14.1 cm
3.3 cm
4.23 cm2
42.3 cm2
46.53 cm2
What should my answer be??
Significant Figure Math Rules
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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
Chemical Compound Quiz
Which is denser: ice or water?
Water
Why??
Ice Expands 1/7th!!!
Significant Figures
Lets’ see if you can:
1. Determine the number of significant figures
needed for an answer involving calculations.
2. Round math problems properly
Significant Figure Math Rules
Remember this 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

0.076 m
Significant Figure Math Rules
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Remember This One:
14.1 cm
3.3 cm
4.23 cm2
42.3 cm2
46.53 cm2
What should my answer be??
47 cm2
Significant Figure Math Rules
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How About This One:
Find the volume?
0.041m high
0.091 m wide
0.034 m deep
0.0001269 m3
What should my answer be??
0.00013 m3
Learning Check
1. 2.19 m X 4.2 m =
A) 9 m2
B) 9.2 m2
2.
3.
4.311 m ÷ 0.07 m =
A) 61.58
B) 62
2.54 m X 0.0028 m =
0.0105 m X 0.060 m
A) 11.3
B) 11
C) 9.198 m2
C) 60
C) 10
Learning Check
In each calculation, round the answer to the
correct number of significant figures.
1. 235.05 m + 19.6 m + 2.1 m =
A) 256.75 m
B) 256.8 m
C) 257 m
2.
58.925 m - 18.2 m =
A) 40.725 m
B) 40.73 m
C) 40.7 m
Euphemisms in Science
We all know that some politicians and government
spokesmen use certain euphemistic phrases to give an
aura of respectability to descriptions of events or actions
which would be offensive when expressed in plain English.
The following is a list of Euphemisms in Science and their
translations into plain English.
“Handled with extreme care during the experiments...”
Not dropped on the floor!