The SI System
Measurements and Calculations
Système Internationale d'Unités (SI)
• an internationally agreed upon system of
measurements.
• Decimal system (all conversions based on
multiples of 10)
• SI consists of seven base units.
Base Unit: defined unit in a system of
measurement that is based on an object or
event in the physical world, and is
independent of other units.
 1 mL = 1 cm3
 1 milliliter is the same
volume as 1 cubic
centimeter.
 1 mL of water has a
mass of approximately
1g
 The mass of 1 milliliter of
water is approximately 1
gram.
 1 L of water has a mass
of approximately 1 kg
 The mass of 1 liter of water
is therefore approximately
1 kilogram.
 1 m3 of water has a mass
of approximately 1 t
 There are 1000 liters in a
cubic meter, so the mass of
1 cubic meter of water is
approximately 1000
kilograms or 1 metric ton.
 Mass of a nickel is 5 g
 A US nickel weighs 5 grams, and a penny
weighs 2.5 grams.
 A typical doorknob is 1 m high
 Although there's no precise standard for
doorknob heights, they're often about 1
meter above the floor.
 The diameter of a CD or DVD is 12 cm
 A CD or DVD is 12 centimeters (120 millimeters) across.
The diameter of the center hole is 15 millimeters.
 1 ha is 1002 m2
 1 hectare is 10 000 square meters, equivalent to the area of a
square 100 meters on a side. A football field is about 100
meters long, so imagine a square the length of a football field
on each side, and that's 1 hectare.
Base Units
 The SI base unit of time is the second (s), based on the
frequency of radiation given off by a cesium-133 atom.
 The SI base unit for length is the meter (m), the distance
light travels in a vacuum in 1/299,792,458th of a second.
 The SI base unit of mass is the kilogram (kg), about 2.2
pounds
SI Base Units
MANY DERIVED UNITS
 Quantity







Unit
Abbreviation
Speed = Length/Time
meter/second
m/s
Volume =(Length) 3
(meter) 3
m3
Density = Mass/Volume kg/m 3
kg/m 3
Acceleration = speed/time
m/s 2
m/s 2
Force = Mass x Acc
kg m/ s 2
N (Newton)
Pressure = Force/Area
kg/m s 2
Pa (Pascal)
Energy = Force x Length kg m 2 / s 2
J (Joule)
Prefix
Symbol
Exponential
yotta
zetta
exa
peta
tera
giga
mega
kilo
hecto
deca
Y
Z
E
P
T
G
M
k
h
da
1024
1021
1018
1015
1012
109
106
103
102
101
no prefix (base unit)
deci
centi
milli
micro
nano
pico
femto
atto
zepto
yocto
d
c
m
m
n
p
f
a
z
y
100
10¯1
10¯2
10¯3
10¯6
10¯9
10¯12
10¯15
10¯18
10¯21
10¯24
Converting between SI Units
 Use the chart like this:
 1 prefixed unit = exponential value of the prefix
 1 cm = 10-2 m
 1 nm = 10-9 m
 1 Mm = 106 m
Example:
Measurements of Length
 Base Unit: the Meter
 Centimeter
 Millimeter
 Nanometer
 Micrometer
 Picometer
Measurement of Mass
 Base Unit: the kilogram (the gram is too small) only prefixed
base unit
Measurement of Time
 Base Unit: the second
Measurement of Temperature
 A measure of how hot or how cold something is
 A quantity that determines the direction of heat flow:
warmer to cooler
 Three temperature scales commonly used:
 Celsius
 Kelvin (absolute)
 Fahrenheit
To Convert F to C and C to F
 1.8 degrees F = 1 degree C
 F = 32 + (1.8 x degrees C)
 Example: Convert 22 degrees C to degrees F
 C=
F – 32/1.8
 Example: Convert 98.6 degrees F to degrees C.
To Convert Celsius to Kelvin
 0 degrees C = 273 K
 K = C + 273
 C = K -273
Examples:
Convert 100 degrees C to Kelvin.
Convert 475 K to degrees C
Convert 250 K to degrees C.
Derived Units
Volume and Density Calculations
Volume
 Base Unit : m 3 Not practical because it is very large
 Commonly used: dm 3 Also called “THE LITER (L)”
 1 dm = 10 cm
 1 cm
3
= 1mL
 1 dm 3 = 1 L
 NOTE: 1 dm 3 = (10 cm) 3 = 1000 mL= 1000 cm 3 = 1L
 Example: Calculate the volume of a cube that is 3.30 cm on
each side.
Density
 Mass to volume ratio
 The mass of a unit volume
 density = mass/volume
 d = m/v
Examples
 Calculate the density of a piece of glass with a mass of
6.65 g and a volume of 2.95 mL.
 Calculate the thickness of an aluminum foil 15.38 cm
long and 14.39 cm wide. The mass of the foil is 1.4939 g.
The density of aluminum is 2.70 g/cm 3 . (HINT: We
consider the Aluminum foil to be a rectangular solid).
Dimensional Analysis (Factor Label)
 Method of calculating using the units
 Makes word problems and chemistry calculations easy!
 Any unit can be converted to another by using appropriate
conversion factors
Appropriate conversion factors
 Come from equality statements
 1 kg = 103 g
 1 hr = 60 minutes
 1 mm = 10-3 m
 Conversion factors (equalities written as fractions)
 Which factor do I use?
 Start unit x final unit = final unit
start unit
Example
 On a picnic, 162 students are each given 2 hot dogs. If there are 9 hot
dogs per pound, priced at $ 4 per 3 pounds, what is the cost of the hot
dogs?
 Note that the following conversion factors can be obtained from the text




of the problem:
1 student = 2 hotdogs
9 hot dogs = 1 lb
$4 = 3 lbs
To begin solving the problem, start with a known and keep your goal in
mind:
 Note that all the units (except $) cancel out!