Chapter 3 Scientific
Measurement
You WILL be able to…
Convert measurements to Scientific notation
Distinguish between accuracy, precision, and error of
a measurement.
List SI units of measurement and common Prefixes
Distinguish between mass and weight of an object
Convert between Celsius and Kelvin
Construct conversion factors
Apply dimensional analysis
Convert complex units
Calculate density of a material
Describe how density varies with temp.
Le Systeme International d’Unites
(SI)
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Also known as the METRIC system
Developed in France in 1795
Based on multiples of 10
Standard of measurements used in the scientific
community and industry in order to speak the
“same language”
Why is it important?
To compare results
To communicate effectively
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5 SI units commonly used by chemists are
the meter, the kilogram, the Kelvin, the
second, and the mole.
SI Unit Prefixes
See table on page 74. Do you recognize any of the Prefixes?
Units and Quantities
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Units of Length - measure of distances, standard
is the meter. This is a FUNDAMENTAL
PHYSICAL QUANTITY
Units of Volume – the amount of space occupied
by an object (substance), standard is the CUBIC
METER (m3 ). This is a DERIVED unit
Units of Mass – of the quantity of matter,
represented by the KILOGRAM
Weight - measure of the gravitational pull on
matter and is NOT an SI base unit! (e.g. scale
activity)
b. standard is the kilogram (why??)
Units and Quantities cont’d
Units of Temperature – measure of average kinetic
energy of particles of matter based on the triple point of
water, standard is the Kelvin
a. This is a FUNDAMENTAL unit
b. The Celsius Scale is commonly used in chemistry
c. To convert Celsius to Kelvin, add 273.15
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Units of Energy – energy is the capacity to do work or to
produce heat
a. this is a DERIVED unit
b. standard is the Joule (J), but calorie is commonly used
c. 1 cal = 4.184J
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Try These!
List the following units in order from
largest to smallest: m3, mL, cL, μL, L, dL
-You should have come up with …
m3 , L, dL, cL, mL, μL
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Which would melt first, germanium with a
melting point of 1210K or gold with a
melting point of 1064 ˚C?
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A MEASUREMENT is a quantity that has both a
number (magnitude) and a UNIT
In chemistry we will deal with extremely large and
small numbers.
We will use scientific notation to deal with these
cumbersome numbers.
Scientific Notation
One number will be represented as the product of
two numbers.
For example:
N x 10y
y is an integer which shows how far to move the
decimal.
If the number is greater than one y is POSITIVE,
move the decimal to the right to expand.
If the number is less than one y is NEGATIVE,
move the decimal to the left to expand.
Try These
Write these in Scientific Notation
 602000000000000000000000
 .000000000000000000000327
Expand the following
3.0 x 108
4.2 x 10-5
How do you enter this into your calculator?
Mathematical Operations Using
Scientific Notation
Addition and Subtraction – can be done
ONLY if the values have the same exponent (n)
 This means that you may have to change one
of the values out of proper scientific notation to
perform the calculation
For example:
a. (5.3 x 104) + (1.3 x 103)
b. (5.3 x 104) - (1.3 x 103)
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a.
b.
= 5.43x104
= 5.17x104
Multiplying and Dividing
Multiplication and Division – can be done
with any values.
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When you MULTIPLY you will ADD the
exponents.
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When you DIVIDE you will SUBTRACT the
exponents.
For Example:
a. (7.2 x 10-4) ÷ (1.8 x 103) =
b. (7.2 x 10-4) x (1.8 x 103) =
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A = 4 x 10-7
B = 1.3
Accuracy, Precision, and Error
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Accuracy – a measure of how close a
measurement comes to the actual or true
value of whatever is measured
(correctness of measurements)
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Precision – a measure of how close a
series of measurements are to one
another (repeatability of measurements)
Precision and Accuracy
Determining Error
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ERROR is the difference between the
experimental value and the accepted value
Error = Experimental Value – Accepted Value
Percent Error takes this difference and divides it
by the accepted value (times 100) to get a
relative error
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Experimentally you determined the boiling
point of octane to be 124.1˚C. The actual
boiling point of octane is 125.7˚C.
Calculate the error and the percent error.
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Use Percent Error =
│error│ X 100
accepted value
This will be used all year LEARN IT!
Significant Figures in
Measurements
What is a Sig Fig?
All the digits in a measurement plus one ESTIMATED digit.
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Rule # 1 – All non-zero digits are significant (23.45)
Rule # 2 – All zeroes between non zero digits are significant (sandwich
rule) (304)
Rule # 3 – Zeroes to the right of a nonzero digit, but to the left of an
unwritten decimal point, are NOT significant. (5000) or (5000.)
Rule # 4 - In numbers less than one, zeros to the right of a decimal
point and to the left of a non-zero digit are NOT significant. (.0034)
Rule # 5 All zeros to the right of a decimal point AND to the right of a
nonzero digit ARE significant (.8400)
TAKE A DEEP BREATH!
Decimal point is PRESENT
0.00026050 mg
Find the first digit & count until the end of the number
Decimal point is ABSENT
870 000 g
Find the first digit & count until the beginning of the number
Apply the Rules to the Following
How many Sig Figs?
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
7.36 cm
85 000 g
29.40 ml
0.00183 s
6 000 000 ˚C
3
2
4
3
1
Math with Sig Figs
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General Rule – A calculated answer cannot be
more PRECISE than the LEAST precise
measurement from which it was calculated
Addition and Subtraction – The answer should
be rounded to the same number of DECIMAL
PLACES (not digits) as the measurement with
the least number of decimals places
Multiplication and Division - When multiplying
and dividing, the answer can have no more SIG
FIGS than are in the measurement with the
FEWEST number of Sig. Figs
ROUNDING
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Rounding – Simplified version is that 5’s round up.
Apply all the rules to the following…
1. 3.29 cm – 1.4 cm =
2. 80500 km X 0.0060 km =
3. Round 629.55 meters to 3 Sig. Figs
1= 1.9 cm
2= 480 km2
3= 630. (note the decimal)
Dimensional Analysis/FactorLabel Method
Dimensional Analysis is treating units of
measure as algebraic terms.
 The factor label method allows you to convert
from one unit to another
-In order to change units you need a
CONVERSION FACTOR.
 A conversion factor is a ratio derived from the
equality between two different units that can be
used to convert from one unit to the other or a
ratio of equivalent measurements.
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Conversion factors are known, verified,
exact quantities therefore, they are NOT
used to determine Sig. Figs in a problem
Sig. Figs in a problem are determined by the
original measurements/ data given
Converting Between Units
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Rule – The smaller number has the larger unit and the
larger number has the smaller unit in a conversion factor
(e.g. 1 km = 1000 m)
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Multi-step Problems – You may need to use several
conversion factors to get from the unit that you have to
the unit that you need. Do this by memorizing the
common conversions only, rather than memorizing every
possible metric conversion.
Sample Problem – The radius of a potassium atom is
0.227nm. Express this radius unit in centimeters.
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If you remember that “nano” is 10-9 and “centi” is 10-2 you
can subtract exponents and do this in one step.
However, if you need to see the steps written out, do the
following:
0.227nm X
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1m
X
1 000 000 000 nm
100 cm
1m
=
Converting Complex Units – This applies to most derived
units which are a combination of quantities. Both the
numerator and the denominator must be changed, so
more than on step is necessary.
Try This One!
Gold has a density of 19.3 g/cm3. What is
the density in kilograms per cubic meter?
 Answer…
 1.93 x 10-4 kg/m3
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Density
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Density is the ratio of mass to volume of a substance
The standard is the kg/m3
Equation: D = m/V
Bunsen Honeydew finds a shiny piece of metal that he
thinks is aluminum. In the lab, he determines that the
metal has a volume of 245.0 cm3 (how did he do that?)
and a mass of 612.00 g. Calculate the density in correct
Sig. Figs. Is the metal aluminum?
Density and Temperature
The density of MOST substances
decreases as temperature increases. List
some examples of this from common
experience.
 Water is an exception which allows for life
on Earth to be possible
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