Words to Know
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Qualitative measurements – results
are in a descriptive, nonnumeric form
(Forehead feels hot)
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Quantitative – results are in a definite
form, usually as numbers or units
(Temperature is 1020 F)
Objectives
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Distinguish among the accuracy,
precision, and error of a measurement
Identify the number of significant
figures in a measurement and in the
result of a calculation
Words to Know
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Accuracy – a measure
of how close a
measurement comes to
the actual or true value
of whatever is measured
(Closeness of a dart to
the bull’s-eye)
Precision – a measure
of how close a series of
measurements are to
one another; depends
on more than one
measurement (The
closeness of several
darts to one anotherreproducibility)
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Accepted value – correct value based on
reliable references (Example: Boiling point
of pure water is 1000C at standard
atmospheric pressure)
Experimental value – value measured in the
lab
Error = experimental value minus accepted
value
Error can be positive or negative number
Practice
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A thermometer measures the boiling
point of pure water at standard
atmospheric pressure. It reads 99.10C.
What is the accepted value?
What is the experimental value?
What is the error?
Ans. – Acc (1000C) Exp (99.10C)
Error is 99.10C – 1000C, or -0.90C
Percent Error (Relative Error)
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Percent error is the absolute value of
the error divided by the accepted
value, multiplied by 100%
Using absolute value means that the
percent error will always be a positive
value
Calculate the percent error for the
boiling pure water
Answer
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Percent error = (absolute value of the
error ÷ accepted value) x 100%
.90C ÷ 100.00C = 0.009
0.009 x 100%
Move decimal point two places to the
right
Answer is 0.9%
Significant Figures
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All the digits that are known, plus a last digit
that is estimated
Every non-zero digit is significant.
Examples: There are three significant
figures in 24.7 meters, 0.743 meters, and
714 meters.
Zeros appearing between non-zero digits
are significant.
Examples: There are four significant digits
in 7003 meters, 40.79 meters, and 1.503
meters.
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Leftmost zeros appearing in front of
non-zero digits are not significant.
They act as placeholders.
Examples: 0.0071 meter, 0.42 meter,
and 0.000099 meter each have only
two significant figures.
Write these numbers in scientific
notation to get rid of placeholding
zeros.
Answers
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Decimal point moves to the right, so all
exponents will be negative numbers
7.1 x 10-3 meter
4.2 x 10-1 meter
9.9 x 10-5 meter
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Zeros at the end of a number and to
the right of a decimal point are always
significant.
Examples: 43.00 meters, 1.010
meters, and 9.000 meters each have
four significant figures
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In a number that has no decimal point, zeros at
the rightmost end of the measurement are not
significant if they serve as placeholders to show
the magnitude of the number.
Examples: 2500 meters 460,000 meters, and
16,000 meters each have 2 significant figures
If such zeros were known measured values,
however, then they would be significant and
should be written in scientific notation.
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Examples: 300 meters and 7000
meters each have one significant
figure
If the zeros are known measured
values, record them as 3.00 x 102
meters and 7.00 x 103 meters
The measurement 27210 has four
significant figures.
Atlantic/Pacific Rule
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If a decimal
point is
present,
count from
this side
starting with
the first nonzero digit
and keep
counting
until there
are no
remaining
digits.
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If a decimal
point is
absent,
count from
this side
starting
with the
first nonzero digit
and keep
counting
until there
are no
remaining
digits.
Measurements with an Unlimited
Number of Significant Digits
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1. Counting
Example: 23 people in the classroom
(Not 22.9 or 23.1)
23.00000000…………………………..
2. Exactly defined quantities
Example: 60 minutes = 1 hour
60.00000000…………………………..
Identify the Number of
Significant Figures
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4.0 x 103
1.67 x 10-8
5201
635.000
22 000
0.00530
200.0
400
218
4755.50
Significant Figures in Calculations
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Calculation cannot be more exact than
the measured values used to obtain it
Example: Find the area of a floor
measures 7.7 meters by 5.4 meters
Each measurement has only two
significant figures
Calculator reads 41.58 square meters
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If the digit immediately to the right of
the last significant digit is less than 5, it
is dropped
If it is 5 or greater, the value of the last
significant digit is increased by 1
41.58 square meters becomes 42
square meters
Practice Problems
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Round each measurement to two
significant figures. Write your answers
in scientific notation.
A. 94.592 grams
B. 2.4232 x 103 grams
C. 0.007 438 grams
D. 54 752 grams
E. 6.0289 x 10-3 grams
F. 405.11 grams
Answers
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A.
B.
C.
D.
E.
F.
9.5 x 101 grams
2.4 x 103 grams
7.4 x 10-3 grams
5.5 x 104 grams
6.0 x 10-3 grams
4.1 x 102 grams
Calculation Rules
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Multiplication and Division – round the
answer to the same number of
significant figures as the measurement
with the least number of significant
figures
Addition and Subtraction – the answer
should be rounded to the same
number of decimal places as the
measurement with the least number of
decimal places