# SI Units and Measurements

```SI Units
SYST&Eacute;ME INTERNATIONAL D&acute;UNIT&Eacute;S
Defining the kilogram
The need for SI Units
 At the end of the eighteenth century, science and




technology were growing by leaps and bounds across the
developed world.
New scientific studies needed to be shared between
countries and needed to have the same units of
measurement in order to be accurately compared
In 1791, the metric system was established in Europe
In 1875, The Metre Convention was established – a group
of international scientists that would get together every
4-6 years to discuss units of measurement
The most recent additional was the mole in 1971
Base Units
UNITS THAT CANNOT BE DERIVED FROM
OTHER UNITS
Mass
 SI Unit: kilogram (kg)
 Original definition (1793) – The
grave was defined as the mass of
one cubic decimetre of pure water at
its densest point (4&deg; C)
 Current definition (1889) – The
mass of the International
Prototype Kilogram or “Big K”
 The Indus Valley Civilization
were the first to develop a system of
weights and measures (4000 BC)
Length
 SI Unit: metre (m)
 Original definition (1793): 1/10,000,000 of the
distance between the North Pole and the equator, in
a line going through Paris
 Current definition (1983): The distance traveled by
light in a vacuum in 1/299,792,458 seconds
 The ancient Egyptians (3000 BC) used the unit
cubit to measure length – the length from the elbow
to the tip of the middle finger. It is believed that
yards, feet, and inches were derived from this.
Time
 SI Unit: second (s)
 Original Definition
(Medieval): 1/86,400 day
 Current Definition (1967): the
time it takes to transition
between two states of
caesium 133
 Ancient calendars marked the
passage of time as early as
6000 years ago
 Ancient time keepers include
Egyptian sundials, Persian
water clocks, and European
hourglasses
Temperature
 SI Unit: kelvin (K)
 Original definition (1743): established the centigrade
scale (&deg;C) by assigning 0&deg;C to the freezing point of
water and 100&deg;C to the boiling point of water
 Current definition (1967): assigned 0 K to absolute
zero – the point at which all atomic motion stops
Amount of a substance
 SI Unit: mole (mol)
 Original definition (1900): The molecular weight of a
substance in grams
 Current definition (1967): The amount of substance
that contains as many “parts” as 0.012 kg of Carbon12
 Avogadro’s number: 6.02 x 1023 molecules per mole
Derived units
Weight
 The force on an object due to gravity
 NOT the same as mass: Weight = mass x gravity
 SI Unit: newton (N)
 The ancient Greek had many definitions of weight:
 Aristotle – weight was the opposite of levity and the two
competed to determine if an object would sink or float. The
earth had ultimate weight and fire had ultimate levity.
 Plato described weight as an objects desire to seek out its kin
 Galileo was the first to determine that weight was related to
the mass of an object
Speed
 SI Unit: meter per second (m/s or ms1)
 Used to describe the time it takes an
object to travel a given distance
Area
 SI Unit: square
meters (m2)
 Used to describe
the space occupied
by a two
dimensional object
Volume
 SI Unit: cubic meter (m3)
 Used to describe the space an object occupies
Density
 SI Unit: kilogram per meter cubed (kg/m3 or kgm-3)
 Describes how compact a substance is
 Density = mass/volume
Energy
 SI Unit: Joule (J) Named after James Prescott Joule
 Energy is the capacity to do work or to produce heat
 Calorie (cal) is the heat needed to raise 1 gram of
water by 1&deg;C
 1 cal = 4.18 J
Prefixes
Larger than the base
 deca – 101
 hecto – 102
 kilo – 103
 mega – 106
 giga – 109
 tera – 1012
10
100
1000
1000000
1000000000
1000000000000
Smaller than base
 deci – 10-1
 centi – 10-2
 milli – 10-3
 micro – 10-6
 nano – 10-9
 pico – 10-12
0.1
0.01
0.001
0.000001
0.000000001
0.000000000001
Making Measurements
HOW TO BE ACCURATE, PRECISE, AND
Making Measurements
 Qualitative – measurements are words, like heavy or
hot
 Quantitative – measurements involve number
(quantities) and depend on:
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
The reliability of the measuring instrument
The care with which it is read (This depends on YOU!)
 Scientific Notation
 Coefficient raised to the power of ten (ex. 1.3 x 107 instead of
13000000)
Accuracy, Precision and Error
 Accuracy – how close a measurement is to the true
value
 Precision – how close the measurements are to
each other (reproducibility)
Neither accurate
nor precise
Precise, but not
accurate
Precise AND
accurate
Accuracy, Precision, and Error
 Accepted value – the correct value based on
reliable references
 Experimental value – the value measured in the
lab by you
 Error – accepted value – experimental value

Can be positive or negative
 Percent error – the absolute value of the error
divided by the accepted value, then multiplied by
100%
Why is there uncertainty?
 Measurements are performed with instruments, and
no instrument can read to an infinite number of
decimal places
 Which of the balances below has the greatest
uncertainty in measurement?
Significant Figures in Measurements
 Significant Figures in a measurement include all
of the digits that are known, plus one more digit that
is estimated
 Measurements must be reported to the correct
number of significant figures
Rules for Counting Significant Figures
Non-zeros always count as
significant figures:
3456 has
4 significant figures
Rules for Counting Significant Figures
Zeros
Leading zeroes do not count as
significant figures:
0.0486 has
3 significant figures
Rules for Counting Significant Figures
Zeros
Captive zeroes always count as
significant figures:
16.07 has
4 significant figures
Rules for Counting Significant Figures
Zeros
Trailing zeros are significant only
if the number contains a
written decimal point:
9.300 has
4 significant figures
Rules for Counting Significant Figures
Two special situations have an
unlimited number of significant
figures:
1. Counted items
a) 23 people, or 425 thumbtacks
2. Exactly defined quantities
b) 60 minutes = 1 hour
Sig Fig Practice #1
How many significant figures in the following?
1.0070 m 
17.10 kg 
100,890 L 
3.29 x 103 s 
0.0054 cm 
3,200,000 mL 
5 dogs 
Significant Figures in Calculations
 In general a calculated answer cannot
be more precise than the least
precise measurement from which it
was calculated.
 Ever heard that a chain is only as
strong as the weakest link?
 Sometimes, calculated values need to
be rounded off.
 Rounding
Decide how many significant figures
are needed (more on this very soon)
 Round to that many digits, counting
from the left
 Is the next digit less than 5? Drop it.
 Next digit 5 or greater? Increase by 1

 Addition and Subtraction
 The
answer should be rounded
to the same number of
decimal places as the least
number of decimal places in
the problem.
 Multiplication and Division
 Round
the answer to the same
number of significant
figures as the least number of
significant figures in the
problem.
Rules for Significant Figures in
Mathematical Operations

Multiplication and Division: # sig
figs in the result equals the number in
the least precise measurement used in
the calculation.
 6.38 x 2.0 =
 12.76  13 (2 sig figs)
Sig Fig Practice #2
Calculation
Calculator says:
3.24 m x 7.0 m
22.68 m2
100.0 g &divide; 23.7 cm3
4.219409283 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2
710 m &divide; 3.0 s
236.6666667 m/s
1818.2 lb x 3.23 ft
5872.786 lb&middot;ft
1.030 g x 2.87 mL
2.9561 g/mL
Rules for Significant Figures in Mathematical
Operations

Addition and Subtraction: The
number of decimal places in the
result equals the number of decimal
places in the least precise
measurement.
6.8 + 11.934 =
18.734  18.7 (3 sig figs)
Sig Fig Practice #3
Calculation
Calculator says:
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 lb + 3.37 lb
1821.57 lb
1821.6 lb
2.030 mL - 1.870 mL
0.16 mL
0.160 mL
*Note the zero that has been added.
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