2.1 Units of Measurement
SI Units
 The SI system (Systeme International d’Units) is the latest of many
metric systems.
Base Units
 7 Base Units in the SI system
 Based on an object or natural event
 If the unit name is based on a person’s name the symbol is
capitalized, but the unit name is not.
Quantity
Unit
Symbol
Length
meter
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Temperature
kelvin
K
Amount of substance
mole
mol
Luminous intensity
candela
cd

SI prefixes
 Prefixes allow scientists to change the magnitude of the unit
without changing the base unit. Prefixes are basically powers of 10
applied to a unit.
Prefix
Symbol
Multiplier
giga
G
1 000 000 000
mega
M
1 000 000
kilo
k
1000
hecto
h
100
deka
da
10
Base Unit
1
deci
d
1/10
centi
c
1/100
milli
m
1/1000
micro
μ
1/1 000 000
nano
n
1/1 000 000 000
Derived Units
 Derived units are units of measure made by combining the seven base
units.
2
 Area – square meters (m )
 length x width
3
 Volume – cubic meters (m )
 length x width x height
3
 SI unit = dm
1 dm3 = 1 liter (liters are not an SI unit)
○ Liters may be abbreviated “l” or “L”
Density – grams / cm3 (g/cm3)
 density = mass / volume
Force – newtons (N)
2
 amount of force required to accelerate 1 kg at a rate of 1 m/s
Pressure – pascal (Pa)
2
 a force of 1 newton per m
Energy – joule (J)
 energy expended in applying a force of 1 newton over 1 meter
distance
Power – watt (W)
 1 joule per second
Frequency – hertz (Hz)
 1 cycle/second
Electric Charge – coulomb (C)
 Amount of electrical charge transported by a current of 1
ampere in 1 second








Problem Solving – A, B, C, D
Analyze the problem.
What is the question really asking?
What units should the answer have?
What given information is important?
Brainstorm ways to find the answer.
List the knowns and unknowns.
Consider ways to use the information to get your answer.
Draw pictures.
Guess & check.
Use an equation / formula.
Calculate your answer
Rearrange equations before substituting.
Find the unknown.
Defend your answer.
Did you get the right units?
Is the answer the right magnitude?
Does the math make sense?
Calculate the final answer twice.
Make sure you write the units!!!
Temperature
 Temperature = average kinetic energy of a sample
of matter (what’s the average speed of the
particles)
 Degrees Celsius – commonly used temperature
scale
o
 0 C = freezing point of water
o
 100 C = boiling point of water
 Kelvins – SI unit of temperature
 The kelvin scale is an absolute scale – there are
no negative values
 0K = absolute zero (there is no possible lower
temperature)
 273K = freezing point of water
 373K = boiling point of water
 Conversion
o
 K = C + 273
o

C = K – 273
o
 Kelvins and C are the same size, just offset by
273
2.2 Scientific Notation and Dimensional Analysis
Scientific Notation
 System used to write very large or very small numbers
 Numbers are expressed as a number between 1 and 10 along with a
multiplier expressed as a whole number power of 10.
 Numbers larger than 1 will have a positive exponent (or 0)
 Numbers less than 1 will have a negative exponent
M x 10n
1 < M < 10 and n is an integer read as M times 10 to the nth
 Addition & subtraction in scientific notation
 Multiplication & division in scientific notation
Dimensional Analysis & the Box Method
 Conversion factors
 Any two equivalent measures may be used to write a ratio with a
value of 1. This ratio is a conversion factor.
 60 min./1 hour or 1 hour/60 min. (both are ratios = 1)
 1000 mL/1 L = 1 = 1 L/1000 mL
 Dimensional Analysis
 Method of converting units using equivalent measures
 The same unit will always be written diagonally in the
expression so that the unit cancels out in the calculation.
 Write as many conversion factors as necessary to get to answer
 Multiply across the top, then divide all the way across the
bottom
Check significant digits (conversion factors don’t count when
calculating sig figs)
○ For example: Convert 145 seconds into minutes.
145 seconds
1 minute
x
= 2.42 minutes
60 seconds
 The Box Method
 Method of converting units similar to dimensional analysis using a
series of boxes.
 Place the measurement you are converting from in the top left
corner of your matrix.
 In the next set of boxes, place a ratio that relates your unit to the
unit you want to convert to, so that the unit you are converting
from cancels out.
 Multiply across the top, then divide all the way across the
bottom.
 Check significant digits (conversion factors don’t count when
calculating sig figs)
○ For example: Convert 145seconds into minutes.
145 seconds
1 minute
= 2.42 minutes
60 seconds

Convert 145 seconds into years
Dimensional Analysis
145 seconds 1 minute
1 hour
1 day
1year
x 60 seconds x 60 minutes x 24 hours x 365 = 4.60 x 10-6 yrs
days
Box Method
145 seconds 1 minute
1 hour
1 day
1year
= 4.60 x 10-6 yrs
60 seconds 60 minutes 24 hours 365 days
2.3 How Reliable are Measurements?
Accuracy & Precision
 Accuracy = comparison of a measure against a known standard
 If you get the number that is expected when compared to a known
standard, the measure is accurate (we calibrate scales to make sure
they are accurate)
 Precision = ability to reproduce the measurement
 If you can reproduce over and over, the measure is said to be
precise
 If a measure is precise and accurate, then it is said to be reliable.
Calculating Percent Error


Comparison of a measurement to its accepted value.
Percent error is calculated using the formula:
measured value – accepted value
Percent Error =
accepted value
x 100
Significant Figures
 Measurements include a number of digits that are certain and always 1
that is uncertain. The last digit in a measurement is always either
rounded or estimated depending on the instrument being used.
 Measurements are never free of uncertainty. They will be uncertain
because:
 measuring instruments are never completely free from error
 measuring always involves some level of estimation
 Making valid measurements
 When using a scaled instrument (rule, meter stick, graduated
cylinder, pipet, buret, etc.) always estimate one place beyond the
certainty of the instrument.
 The human eye is very capable of estimating a tenth of a unit on
most scaled instruments used in the lab.
25.45 cm

What is a significant digit?
 The certain digits and the estimated digit of a measurement are
together significant for a measurement.
 Rules for identifying sig figs.
 Non-zero digits are always significant.
 Zeros between non-zero digits are always significant.
 Final zeros after the decimal point are always significant.
 Zeros used as placeholders are not significant.
 Counts and defined constants have an infinite number of
significant digits.
 How many sig figs?
 96g
 5.029m
 61.4g
 306m
 0.52g
 7000mL
 4.72km
 0.00783L
 4.7200km
 6500.mL
 82.0km

60 when used in 60 min = 1 hr
Rounding Off Numbers
 When making calculations numbers must be rounded so that they do
not give the illusion of extreme precision.
 Rules for Rounding Numbers
 If the digit(s) to the right of the last significant digit is (are)
 less than five, round the significant digit down,
○ 5.543 → 5.54 or 3.27499 → 3.27
 greater than five, round the significant digit up,
o 5.546 → 5.55 or 3.27501 → 3.28
 equal to exactly five, round the significant digit to be even.
o 5.545 → 5.54 or 3.275 → 3.28
 Rounding in Calculations
 Addition & Subtraction
 The answer may contain only as many decimal places as the
measurement having the least number of decimal places.
 Multiplication & Division
 The answer may contain only as many significant digits as the
measurement with the fewest significant digits.
2.4 Representing Data
Graphing
 Pie charts
 Used to represent categorical data as parts of a whole. Pie charts
typically depict percentages (fractions). A pie chart is constructed
by converting the share of each component part into a percentage of
360o.
 Bar Graphs
 Used to represent categorical or numeric values within certain
intervals. Bars may be drawn horizontally or vertically. Each bar
represents a category, value or range of values. They are often used
to show changes over time and clearly illustrate differences in
magnitude.
Line Graphs
 Most common graph used in science. They show the relationship
between two variables. Line graphs are useful for showing trends.
 Relationships are shown using best-fit lines which may not intersect
any of the data points.
 The slope of the line may be calculated using the formula
slope = ∆y / ∆x
where ∆ means “change in”.