Transcript Accuracy and Precision - Lyndhurst School District

Scientific
Measurement
Chapter 3
Sections
3.1 Measurements and Their Uncertainty
 3.2 The International System of Units (SI)
 3.3 Conversion Problems
 3.4 Density

3.1 Vocabulary
-International System
of Units (SI)
- meter (m)
- liter (L)
- kilogram (kg)
- gram (g)
- weight
- temperature
-
-
Celsius scale
Kelvin scale
absolute zero
energy
joule (J)
calorie (cal)
3.1 Measurements and Their Uncertainties

OBJECTIVES
-What is accuracy and precision ?
-What are significant figures and how do
you work with measurements?
CHEMISTRY
& YOU
How do you measure a photo finish?
Sprint times are often
measured to the
nearest hundredth of a
second (0.01 s).
Chemistry also requires
making accurate and
often very small
measurements.
A measurement is a quantity that has
both a number and a unit.
 Your
height (66 inches), your age
(15 years), and your body
temperature (37°C) are examples
of measurements.
Do Now
Why do we use scientific notation?
• Large and small numbers can be written in
shorthand form
 This makes it easier to see the number
clearly and work with
• The width of a DNA helix is – 0.0000000034 meters
or 34 angstroms
• When discussing the large amount of the US debt
$17,000,000,000,000
• Distance between Earth and Sun
92,960,000 miles
In chemistry, you will often encounter very
large or very small numbers.

A single gram of hydrogen, for example, contains
approximately 602,000,000,000,000,000,000,000
hydrogen atoms.
You
can work more easily with very
large or very small numbers by
writing them in scientific notation.
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its affiliates. All Rights Reserved.
Scientific Notation
Mx
M
n
10
is the coefficient 1<M<10
 10 is the base
 n is the exponent or power of 10
Numbers greater than 1 will have a
positive exponent
54,500
5.45 x 104
How to plug into calculator:
5.45E4
10^4
5.45 x
Numbers less than 1 will have a
negative exponent.
0.000001
1 x 10-6
Write in Scientific Notation
Answers
1)
5,200
1)
5.2 x 103
2)
0.00023
2)
2.3 x 10-4
3)
43
3)
4.3 x 101
4)
0.00000872
4)
8.72 x 10-6
5)
78,900,000
5)
7.89 x 107
Write as whole numbers
Answers
1)
5.32 x 105
1)
532,000
2)
9.17 x 10-3
2)
0.00917
3)
4.3 x 10-8
3)
0.00000043
Calculations with Scientific Notation
1. Addition and Subtraction
Before numbers in scientific notation can be
added or subtracted, their exponents must be
equal
Move decimal point left to increase exponent
Move decimal point right to decrease exponent
Practice Problems
1)
(7.5 x 103) + (2.0 x 104)
2)
(9.52 x 104) + (3.1 x 105)
3)
(8.083 x 104) + (2.5 x 106)
Practice Problems
4)
(2.5 x 103) – (3.0 x 102)
5)
(4.62 x 105) – (2.0 x 104)
Addition and Subtraction
Scientific
Notation
For example, when adding 5.4 x 103 and
8.0 x 102, first rewrite the second number
so that the exponent is a 3. Then add the
numbers.
(5.4 x 103) + (8.0 x 102)
= (5.4 x 103) + (0.80 x 103)
= (5.4 + 0.80) x 103
= 6.2 x 103
Scientific Notation
https://www.youtube.com/watch?v=Xz6cYr5t
He0
2. Multiplication
Multiply the numbers, add the exponents
Example:
(2.00 x 103)(4.00 x 104)
= 8.00 x 107
Examples
A)
(2.0 x 104)(2.5 x 102)
B)
(3.3 x 103)(1.5 x 10-5)
3. Division
Divide the numbers, subtract the exponents
Example:
(9.00 x 107)
(3.00 x 104)
= 3.00 x 103
Examples
A) (8.0 x 104)
(4.0 x 102)
B) (3.0 x 10-3)
(2.0 x 10-2)
Accuracy, Precision, Error
Accuracy, Precision,
and Error
Accuracy and Precision
In chemistry, the meanings of accuracy and
precision are quite different.
 Accuracy
is a measure of how close a
measurement comes to the actual or true
value of whatever is measured.
 Precision
is a measure of how close a series
of measurements are to one another,
irrespective of the actual value.
Accuracy, Precision,
and Error
Accuracy and Precision
Darts on a dartboard illustrate the
difference between accuracy and
precision.
Good Accuracy,
Good Precision
Poor Accuracy,
Good Precision
Poor Accuracy,
Poor Precision
The closeness of a dart to the bull’s-eye corresponds to the degree of
accuracy. The closeness of several darts to one another corresponds to the
degree of precision.
a)
b)
c)
Determine precision and accuracy
Example: Accuracy
 Who
is more accurate when
measuring a book that has a true
length of 17.0cm?
Jennifer:
17.0cm, 15.0cm, 14.0cm, 14.5cm
Lawrence:
17.2cm, 17.0cm, 16.9cm, 17.3cm
Example: Precision
Who is more precise when measuring
the same 17.0cm book?
Tom:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Brady:
15.4cm, 15.0cm, 15.2cm, 15.3cm
Accuracy, Precision,
and Error
Determining Error
Suppose you use a thermometer to measure
the boiling point of pure water at standard
pressure.
The
thermometer reads 99.1°C.
The
true or accepted value of the boiling
point of pure water at these conditions is
actually 100.0°C.
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its affiliates. All Rights Reserved.
Determining Percent Error
accepted value - the correct value for the
measurement based on reliable references
experimental value - the value measured in
the lab.
% Error= |experimental –accepted| x100
accepted value
Sample Problem 3.2
Substitute the equation for error, and then plug
in the known values.
|experimental
value – accepted value|
_______________________________
Percent error =
accepted value
|99.1°C – 100.0°C|
=
X 100%
100.0°C
=
0.9°C
_______
100.0°C
X 100 % = 0.9%
X 100%
Significant Figures
 The
significant figures in a
measurement include all of the
digits that are known, plus one
last digit that is estimated.
Centimeters and Millimeters
Graduated Cylinder - Meniscus
Rules for Significant Figures
1) ALL non-zero numbers (1,2,3,4,…) are
ALWAYS significant.
Ex. 1.314 g
---> 4 significant figures
2) ALL zeroes which are to the left of
nonzero digits are NOT significant.
Ex.
0.0025
---> 2 s.f.
Rules for Significant Figures
3) ALL zeroes between non-zero numbers
are ALWAYS significant.
Ex.
1.008
---> 4 s.f.
4) ALL zeroes which are to the right of the
decimal point are ALWAYS significant.
500.0
---> 4 s.f.
500
---> 1 s.f.
How many significant figures are there?
Answer
a) 12.5
b) 70.52
c) 0.00604
d) 0.896
e) 7200
f) 3001.2
g) 450.0
a)
b)
c)
d)
e)
f)
g)
3
4
3
3
2
5
4
s.f.
s.f.
s.f.
s.f.
s.f.
s.f.
s.f.
Rounding with Significant Figures
If the digit to be removed
a. is less than 5, the preceding digit stays
the same.
Ex: 1.33 rounds to 1.3
b. is equal to or greater than 5, the
preceding digit is increased by 1
Ex: 1.36 rounds to 1.4
Calculations with Significant Figures
The resulting answer can never be more
precise than the least precise measurement
in the calculation.
How many sig figs?
100
10302.00
0.001
10302
1.0302x104
Sig Figs in Addition/Subtraction
The result has the same number of
decimal places as the number in the
operation with the least decimal
places.
Ex: 2.33 cm
+3.0 cm
5.3 cm
Sig Figs in Multiplication/Division
 The
answer has the same sig figs as
the factor with the least sig figs.
 Ex: 3.22 cm
x 2.0 cm
6.4 cm2
3.2 International System of Units
and
Prefixes
Math and Units
 Math-
the language of Science
 SI Units – International System
 MKS
Meter m
Mass kg
Time s
 National Bureau of Standards
 Prefixes
Base SI Units
Symbol
Quantity
Unit
Length
meter
m
Mass
kilogram
kg
Temperature
kelvin
K
Time
second
s
Amount of
mole
Substance
Luminous Intensity candela
mol
Electric Current
a
ampere
cd
SI Unit Prefixes
Name
gigamegakilodecicentimillimicronanopico-
Symbol
G
M
k
d
c
m
μ
n
p
109
106
103
10-1
10-2
10-3
10-6
10-9
10-12
Units for Length
km
1 km = 1,000 m
(m) meter
1 m = 1,000 mm
cm
Mm
Units for Volume
m3
cm3
1 dm3 = 1L
dm3
1cm3= 1mL
L
mL
Liter
Units for Mass
kg
g
1 dm3 = 1L
mg
1cm3= 1mL
μg microgram
Temperature
A measure of how hot or how cold an
object is.
SI Unit: the kelvin
 Note:
not a degree
 Absolute Zero= 0 K
(K)
Temperature Scales
Celsius and Kelvin
K= oC + 273
Farenheit and Celsius
oF=
(1.8 oC ) +32
Units for Energy
 Joule
 calorie
J
1 cal= 4.184 J
1 cal = quantity of heat needed to raise
the temp of 1g of water by 1 oC.
Note:
1 Cal = 1kcal =1000cal
SI Unit Prefixes
Name
gigamegakilodecicentimillimicronanopico-
Symbol
G
M
k
d
c
m
μ
n
p
109
106
103
10-1
10-2
10-3
10-6
10-9
10-12
3.3 Conversion Problems
Factor Label Method of Unit
Factor-Label Method
 Example:
Convert 5km to m:
NEW UNIT
5km x 1,000m =5,000m
km
OLD UNIT
Convert 7,000m to km
7,000m x 1 km = 7 km
1,000m
Convert 2.45cs to s
 2.45cs
x 1s
= 0.0245s
100cs
Convert 55.00 km/h to m/s
55.00 km x 1000 m x 1 h___ = 15.28m/s
h
1 km
3600 s