SI System and
Unit Conversions
What makes a measurement useful?
• It must include a number and a unit.
• A standard must be used
– An exact quantity that people agree to use for
comparison.
2
SI System
• Scientists use SI system
– International System of Units
– SI comes from the French
• “Systeme International d’Unites”
– revised version of the metric system
3
SI Standard Units
Quantity
Standard Unit
Symbol
Length
meter
m
Mass
kilogram
kg
Temperature
Kelvin
K
Time
second
s
Amount of substance
mole
mol
Electric Current
ampere (amp)
A
Luminous Intensity
candela
cd
The SI system is built on these 7 units, each of which have a standard. All other SI
units can be derived from these.
4
Derived SI units
• Any combination of SI units such as
– g/cm3
– m/s2
– Newton (N)
5
Common SI derived units
Quantity
Unit
symbol
Area
Square meter
m2
Volume
Cubic meter
m3
Density
Kilograms per cubic meter
kg/m3
Pressure
Pascal (kilogram per meter Pa (kg/m•s2)
second squared)
Energy
Joule
J
(kg•m2/s2 )
Force
Newton
N
(kg•m/s2)
Frequency
Hertz (cycles per second,
reciprocal second))
Hz
(1/s or s-1)
Electric charge
Coulomb (ampere second)
C
(A•s)
6
Non SI units commonly used in science
Quantity
Unit
Useful
relationships
Example
Volume
Liter (L)
1L=1000cm3
1mL=1cm3
1L approximately
equals a quart
1mL≈ 20 drops H2O
Energy
calorie (cal)
1cal=4.184J
1J=0.2390cal
Amount of heat
that raises the
temperature of 1g
of H2O by 1◦C
Temperature
Celsius, C
Fahrenheit, F
K=◦C + 273
◦C=5/9 (◦F - 32)
◦F=9/5◦C +32
Water freezes at
273K, 0◦C, and 32◦F
Water boils at 373K,
100◦C, and 212◦F
7
Prefixes
• Base units are not always convenient
– For very large or very small values
• Represent measurements in a more compact
way with the use of prefixes
8
• Example
– The time it takes for a computer hard drive to read
or write data might be 0.009 seconds.
– We can more conveniently represent this time as
9 milliseconds, where the prefix “milli” means
“thousandth”
• So 9 milliseconds means 9 thousandths of a second, or
0.009 seconds
9
SI Prefixes
Prefix
Symbol
Meaning
giga-
G
Billion (109)
mega-
M
Million (106)
kilo-
K
Thousand (103)
hecto-
H
Hundred (102)
deka-
da
Ten (101)
deci-
d
Tenth (10-1)
centi-
c
Hundredth (10-2)
milli-
m
Thousandth (10-3)
micro-
μ
Millionth (10-6)
nano-
n
Billionth (10-9)
pico-
p
Trillionth (10-12)
femto-
f
(10-15)
10
Examples to remember: length
Unit
Example
Kilometer (km)
Length of about 5 city blocks
Meter
Height of doorknob from floor
Decimeter
Diameter of a large orange
Centimeter
Width of a shirt button
Millimeter
Thickness of a dime
Micrometer
Diameter of a bacterial cell
Nanometer
Thickness of an RNA molecule
11
Examples to remember: volume
Unit
Example
Liter (L)
Quart of milk
Milliliter (mL)
About 20 drops of water
Cubic centimeter (cm3)
Cube of sugar
Microliter (μL)
Crystal of table salt
12
Examples to remember: mass
Unit
Example
Kilogram (kg)
Small textbook
Gram (g)
Dollar bill or paper clip
Milligram (mg)
Ten grains of salt
Microgram (μg)
Particle of baking powder
13
Converting SI units
• The SI system is based on powers of 10
– units can be converted by simply moving the
decimal
14
King Henry’s Daughter Barbara Drinks Chocolate Milk
kilo
hecto
deka
Base
deci
(No prefix)
centi
milli
15
To convert a unit by moving the
decimal…
1. Find the prefix of the given measurement on the chart
2. Count over to the right or left to reach the desired unit
3. Move the decimal the same direction and same number
of places
Example:
Convert 360 g to mg
1. Start at the base unit grams
2. Count over 3 steps to the right to reach milli3. Move the decimal 3 places to the right
360.000 so 360,000mg
16
• Example
45.2cg = _____kg
1. Start at the prefix centi2. Count over 5 steps to the left to reach kilo3. Move the decimal 5 places to the left
00045.2 so 0.000452kg
17
Temperature
• Related to the average kinetic energy of the
particles in a sample of matter
• a physical property that determines the
direction of heat flow
• Heat flows spontaneously from a substance at
a higher temperature to a substance at a
lower temperature
18
Temperature Conversions
• Three temperature scales
– Fahrenheit (⁰F)
• U.S. commonly uses (weather, oven temperatures, etc)
– Celsius (⁰C)
• Most other countries commonly use
• This is the scale we use in lab
– Kelvin (K)
• “absolute” temperature scale
• O Kelvin is called absolute zero- the lowest possible
temperature when molecular motion ceases, particles have
no kinetic energy
19
Temperature
Scale
Water Freezes
at
Water Boils at
Body
Temperature
Absolute Zero
Fahrenheit
32◦F
212◦F
98.6◦F
-460◦F
Celsius
0◦C
100◦C
37◦C
-273◦C
Kelvin
273 K
373 K
310 K
OK
Note that the degree symbol is not used with the Kelvin scale. When reading
a Kelvin temperature, the correct way is to say “273 Kelvin” instead of “273
degrees Kelvin”.
20
Temperature conversions
• Use the following equations to convert from
one temperature scale to another.
Conversion
Formula
Celsius to Kelvin
K = C + 273
Kelvin to Celsius
C= K - 273
Fahrenheit to Celsius
C = (F – 32) x 5/9
Celsius to Fahrenheit
F = (C x 9/5) + 32
*To convert between Kelvin and Fahrenheit is a two step process.
Convert to Celsius first, then to Kelvin or Fahrenheit.
21
English Units
• Most of us in the U.S. grow up using English
units such as pounds and inches.
• To convert between English units or between
English and metric units, you must use a
method called dimensional analysis.
22
Dimensional Analysis
• Equality statements such as 1ft=12in. are
made into fractions and then strung together
in such a way that all units except the desired
one are canceled out of the problem
23
• Keeping track of units can help you
– convert one measured quantity into its equivalent
quantity of a different unit
– Set up a calculation without the need for a
formula
24
To set up a conversion problem…
1. write down all “=“ statements you know that
will help you get from the given unit to the new
unit
– Look for equalities given in the problem
•
Example
How many inches are in 1.25 miles? (There are 5,280ft in
1mile.)
“=“ statements:
Given: 5,280ft=1mile
Other: 12in=1ft
25
2. Make fractions out of your “=“ statements. There are 2
fractions for each “=“ that are reciprocals of each
other. These fractions are called “conversion factors”
• Example
5,280ft=1mile
12in.=1ft
5,280ft or 1mile
1mile
5,280ft
12in
1ft
or 1ft
12in
26
3. Begin solving the problem by writing the given
amount with units on the left side of your paper
then choose the fractions that will let a
numerator unit be canceled with a denominator
unit and vice versa until all units are canceled
except the desired unit
Example
1.25miles x 5,280ft x 12in =_______in
1mile
1ft
27
4. Using your calculator, read from left to right and
enter the numerator and denominator numbers
in order. Precede each numerator with a
multiplication sign and each denominator with a
division sign.
Example
1.25miles x 5,280ft x 12in =_______in
1mile
1ft
On your calculator: 1.25x5280/1x12/1=
28
5. Round your calculated answer to the same
number of significant digits your original given
number had. (conversion factors are exact
numbers and so don’t affect the number of
sig. digits)
Example
1.25miles x 5,280ft x 12in = 79,200 in
1mile
1ft
29
example
• Suppose your automobile tank holds 23
gallons and the price of gasoline is 33.5¢ per
liter. How many dollars will it cost you to fill
your tank?
• From the problem, 33.5¢ = 1L
• From a reference table, 1L=1.06qt
4qt=1gal
30
More complex problems…
• Measurements may contain
– More than one unit, such as miles/hr
– fractional or exponential units such as cm3
• treat each unit independently
• Structure your conversion factors to ensure the
given units cancel with a numerator or
denominator as appropriate and the answer ends
with the appropriate unit
• Remember information given in the problem can
be an equality
31
• A car is traveling down the interstate at a
speed of 70 miles per hour (70miles/1hr).
Convert this speed to m/s.
32
Squared and cubed units
• Squared and cubed units are potentially tricky
• For example, remember that a cm3 is really a
cm x cm x cm
• If we were going to convert cm3 to mm3
– We need to use the conversion factor 1cm=10mm
three times (or cube it) so that all three
centimeter units cancel out
33
• One liter is exactly 1000cm3. How many cubic
inches are there in 1.0L?
• 1000cm3=1L
• 1in=2.54cm
34