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Data Analysis
Chapter 2
Units of Measurement

Is a measurement useful without a unit?
SI Units
The metric system is used worldwide.
 Long ago, inexact measurements were
used. For example:
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 Boundaries
would’ve been marked off by walking &
counting the number of steps.
 Time was measured with a sundial or an hourglass
filled with sand.
SI Units
The metric system was adopted in 1795
by a group of French scientists.
 In 1960, an international committee of
scientists met to update the metric system.
Called the SI system (Systeme
Internationale d’Unites)
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Base Units
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There are 7 base units in SI. A base unit is a
defined unit in a system of measurement that is
based on an object or event in the physical
world.
The base unit for:
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Time is second…
Length is meter…
Mass is kilogram…
Temp is…
electrical current is…
amount of sub is…
luminosity is…
The prefixes used with SI units are …(table 2-2)
Derived Units
A derived unit is a unit that is defined by a
combination of base units.
 Example: speed is meters/second (m/s)
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Get out your calculators!
Volume
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Volume is the space occupied by an object.
1 L= 1 dm3
1 mL= 1 cm3
You would use a graduated cylinder to
measure the volume of a liquid in the lab.
You would measure length x width x height
to find the volume of a “regular” solid.
How would you find the volume of an
irregular solid?
Density
Density of a ratio that compares the
mass of an object to its volume
 D=m/v
 Ex 1 Calculate the density of a piece of
aluminum that has the mass of 13.5g &
a volume of 5.0cm3. What is this substance?
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Ex 2 Suppose a sample of aluminum
(Al) is placed in a graduated cylinder
containing 10.5 mL of water & rises to
13.5 mL. What is the mass of the
aluminum sample? (Use the density from
example 1)
Density
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Density of a substance is a property
that doesn’t change, UNLESS altered
by an outside substance.
at STP is 0.998 g/cm3
 Dwater at 4°C is 1.00 g/cm3
 Dwater
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** practice problems #1-3
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If we know the Density & dimensions of a
cube, can we determine the mass of the
cube?
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If the Dair= 0.00122 g/cm3, then what is the
mass of air in this room?
Temperature
Temperature is the measure of how
hot/cold an object is relative to other
objects.
 Scales of temperature:
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Celsius- derived by Anders Celsius & used
the point at which water freezes & boils to
establish his scale
 Freezing
point- 0° C
 Boiling point- 100° C
Temperature
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Kelvin (K)- derived by William
Thomson, known as Lord Kelvin
Kelvin is the SI base unit of temperature
 Conversion process of Celsius to Kelvin
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 Add
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273
Conversion process of Kelvin to Celsius
 Subtract
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Ex.
273
**Practice problems 4-6
4. Convert 357°C to Kelvin
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5. Convert -39°C to Kelvin
6. Convert 266 K to Celsius
Scientific Notation
Scientific notation- expresses a number
as a number between 1 & 10 and then
raised to a power, or exponent.
 When a number is more than one, the
exponent is positive.
 If less than one, the exponent is
negative.
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Scientific Notation
How do we convert data into Sci. Not. ?
 Move the decimal until you have a
number between 1 & 10.
 The exponent in the number of times you
moved the decimal.
 Put unit with answer.
Scientific Notation
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1.
2.
3.
4.
** Practice problems 1-8
700 m
38 000 m
4 500 000m
685 000 000 000 m
5.
6.
7.
8.
0.0054 kg
0.000 006 87 kg
0.000 000 076 kg
0.000 000 000 8 kg
Calculations with Sci Not.
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How do we add/subtract using
Scientific Notation?
Make sure exponents are the same.
 If the exponent is too large, decrease it &
move the decimal that many times to the
right.
 If the exponent is too small, increase it &
move the decimal that many places to the
left.
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Calculations with Sci Not.
Ex. What is 2.70 x 107 + 15.6 x 106?
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** practice problems 5-8
5.
1.26x104 kg + 2.5x103 kg
6.
7.06x10-3 kg + 1.2x10-4 kg
7.
4.39x105 kg – 2.8x104 kg
8.
5.36x10-1 kg – 7.40x10-2 kg
Calculations with Sci Not.
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How do we multiply/divide using sci.
not.?
Multiply/divide the factors(aka
coefficients) first.
 Multiplication
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 Add
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the exponents.
Division
 Subtract
the exponent of the denominator from
the exponent of the numerator.
Calculations with Sci Not.
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Ex.1 What is (2 x 103) x (3 x 102)
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Ex. 2 What is (9 x 108) / (3 x 10-4)
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** practice problems 9-16.
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9.
10.
11.
12.
13.
14.
15.
16.
(4x102 cm)x(1x108 cm)
(2x10-4 cm)x(3x102 cm)
(3x101 cm)x(3x10-2 cm)
(1x103 cm)x(5x10-1 cm)
(6x102 g)/(2x101 cm3)
(8x104 g)/( 4x101 cm3)
(9x105 g)/ (3x10-1 cm3)
(4x10-3 g)/(2x10-2 cm3)
Dimensional Analysis
Dimensional analysis- method of problemsolving that focuses on the units used to
describe matter; often uses conversion
factors.
 Conversion factor- ratio of equivalent
values used to express the same quantity
in different units.
 Ex 1 How many hours are in one year?
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Conversion Factors
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Giga
Mega
Kilo
Hecto
Deca
BASE
Deci
Centi
Milli
Micro
Nano
(Angstro)
Pico
Dimensional Analysis
• Ex. 1 How many meters are in 48 km?
Practice:
• What conversion factor should be used
for the following conversion?
• A. 360 s  ms
• B. 4800 g  kg
• C. 6800 cm  m
Practice using dimensional analysis
1. 4.5 L = __________mL
2. 0.095mg = ____________cg
3. 9500 mm = ___________m
4. 0.575 km = ___________m
5. 100 cm = ___________mm
**Handout “Unit Conversion…”
Conversion
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Ex. 2 What is the speed of 550 meters
per second in kilometers per minute?
Practice
6) How many seconds are there in 24.0 hours?
 86,400 s
7) the density of gold is 19.3 g/mL. What is gold’s
density in decigrams per liter?
 193,000dg/L
8) A car is travelling 90. kilometers per hour. What
is the speed in miles per minute? (1 km=0.62 mi)
 0.93 mi/min
Reliability
How reliable are measurements?
 Accuracy & Precision:
 Accuracy- refers to how close a
measured value is to an accepted
value.
 Precision- refers to how close a series
of measurements are to one another.
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Accuracy or precision
Percent Error
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Percent error- ratio of an error to an
accepted value.
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% error= accepted(book value) – exp (you) x 100
accepted
 % error= (error/accepted) x 100
 Ignore the negative sign, only the
amount of error matters.
Percent Error
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Ex. You calculated the length of a steel
pipe to be 5.2 m. The accepted length is
5.5 m. What is the percent error?
Practice #1
 The accepted density for Cu is 8.96
g/mL. Calculate the percent error for
the measurement 8.86 g/mL.
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**Worksheet**
Significant Figures
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Significant figures- include all known
digits plus one estimated digit.
Rules:
1.
Non-zero numbers are always significant
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2.
Ex. 72.3
Ex. 700
“Sandwich zeros” are significant.
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60.5
809
30.07
Significant Figures
3. Final zeros after the decimal are significant.
a) 6.20
b) 9.00
c) 92.0
d) 0.009200
4. “Place holding” zeros are not significant.
e) 0.095
f) 300
g) 50
h) 30,000
Significant Figures
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You can convert to scientific notation to
remove place holders.
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30,000 = 3 x 104
Example: Determine the number of sig figs in
the following masses.
a) 0.000 402 30 g
b) 405 000 kg
c) 8.20 x 107
*** practice problems p39 # 31 & 32
Rounding Off Numbers
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Rounding to 3 sig figs
2.5320 if the 4th sig fig is <5, do not change
the 3rd sig fig.
 2.5360 if the 4th sig fig is =>5, then round
the 3rd sig fig up.
 Examples:
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(4 sf)
 32.065 (2 sf)
 87.62 (1 sf)
 36,549,555 (2 sf)
 55.845
Addition/subtraction with sig figs
Your answer must have the same number
of digits to the right of the decimal as the
measurement with the FEWEST digits to
the right of the decimal.
 Ex. Add the following measurements: 28.0
cm, 23.538 cm, 25.68 cm.
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** practice problems
Multiplication/division w/ sig figs
Your answer must have the same number
of sig figs as the measurement with the
fewest sig figs.
 Ex. Calculate the volume of a rectangular
object w/ the following dimensions:
length= 3.65 cm,
 width= 3.2cm,
 height= 2.05 cm.
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Multiplication/division w/ sig figs
**practice problems 7-14
 Check old worksheets
 **worksheet**
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Representing Data
Graph- visual display of data
 Circle graph- usually used to represent
percentages of something.
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Representing Data
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Bar graph- often used to show how a
quantity varies with factors such as time,
location, or temperature.
Independent variable- located on the x-axis
 Dependent variable- located on the y-axis
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Bar Graph
3.5
6.00
3
5.00
2.5
4.00
2
3.00
1.5
2.00
1
0.5
1.00
0
0.00
Aug- Sep- Oct- Nov- Dec- Jan- Feb- Mar08 08 08 08 08 09 09 09
Head capsule Size (mm)
Number of Individuals
Progomphus Size vs. Time
#
high
low
mea
Representing Data
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Line Graph- most often used in chemistry
The points on a line graph represent the
intersection of data for 2 variables.
 Independent variable- located on the x-axis.
 Dependent variable- located on the y-axis
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Best fit line- line drawn so that as many
points fall above the line as fall below it.
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Straight best fit- there is a linear relationship
 The
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variables are directly related
Curved best fit- there is a nonlinear
relationship.
 The
variables are inversely related
Interpreting Data
First thing, ID the variables; independent &
dependent
 Notice what measurements were taken
 Decide if the relationship of the variables
is linear/nonlinear.
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