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!
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