SKILLS: SCIENTIFIC NOTATION & METRIC CONVERSION
Scientific Notation
Scientific notation is often used to express either very large or very small numbers. It is based on the use of
exponents. A number between one and ten is followed by 10 raised to a power.
For example, 299 800 000 m/s in scientific notation is 2.998  108 m/s. The power term 108 tells you to move the
decimal over 8 places to the right to return to the standard (common) form.
The 2.998 is called the coefficient.
The coefficient must be a number between 1 and 10 (i.e. there must be one digit before the decimal place).
The 108 is called the power. It consists of the base 10 (always 10 for scientific notation) and the exponent 8.
The exponent shows how many places (and which direction; negative = left, positive = right) the decimal must
move to return to standard (common) form.
As another example, 0.000 15 mm in scientific notation is 1.5  10-4 mm. The power term 10-4 tells you to move the
decimal over 4 places to the left to return to the standard (common) form.
Note that the leading and trailing zeros are dropped as they are merely placeholders (more on this in the Significant
Digits section).
1. Express the following in standard form.
(a) 1.50  108 km
(c) 4.301  104 L
(b) 1.2  10-2 g
(d) 2.2  105 m
2. Express the following in scientific notation.
(a) 300 500 m
(c) 45 000 000 mm
(b) 45.43 mL
(d) 0.000 019 g
The Metric System
Most countries and scientific communities have agreed
on the use of one system of measurement, making
worldwide communication much more efficient. This
system is called “le Système international”, or SI for
short. SI is based on the metric system. Base units are
used, and prefixes are added to change the base unit
by multiples of ten.
SI Base Units
Measurement
Base Unit
Symbol
mass
kilogram
kg
length
metre
m
temperature
Kelvin
K
time
second
s
Common Metric Prefixes
Conversion from one unit to another is relatively easy if
you know the meaning of the prefixes. The table below
shows the prefixes, their symbols, and their meanings.
electric current
ampere
A
amount of substance
mole
mol
intensity of light
candela
cd
A kilometre for example is equal to 1000 m and 1
millimetre is 0.001 m, or 1 m = 1000 mm.
* The kilogram is the only base unit that contains a prefix. The
gram is too small for practical purposes.
12.4 m = 1240 cm
Prefix
Symbol
Factor
giga
G
109
mega
M
106
kilo
k
103
hector
h
102
deca
da
101
Note however that after kilo and milli, each step on the table
represents 3 steps for the decimal point.
Going up the table
move the decimal to
the left
To convert from one unit to another, you simply move the
decimal (left or right) corresponding to the conversion factor.
For example, to convert 12.4 m to centimetres (metres 
centimetres), you move down 2 steps on the table, so the
decimal moves 2 places to the right.
For example, to convert 0.253 MW to megawatts (megawatts
 watts), you move three steps on the table to get to kilo,
then to mega represents an additional jump of three, for a
total of 6 decimal places to the right.
deci
d
10-1
centi
c
10-2
milli
m
10-3
micro
μ
10-6
nano
n
10-9
Going down the table
move the decimal to
the right
NO PREFIX
0.253 MW = 253 000 W
Or, you can realize that the prefix mega- means “ x 106 ”, so you can use this factor to express the measurement in
scientific notation, then convert to standard form.
0.253 MW = 0.253 × 106 W
= 253 000 W
3. Convert the following.
(a) 4.8 g =
kg
(c) 765 nm =
m
(b) 36 000 cm =
m
(d) 1.67 kN =
N
Scientific Notation and Metric Conversion Review
4. Express the following in standard form.
(a) 3.2  105
(d) 8.791  102
(b) 3.2  10-5
(e) 4.96  10-4
(c) 3.2  101
(f) 3  108
5. Express the following in scientific notation.
(a) 14 500
(d) 0.000 056 34
(b) 0.000 42
(e) 960 000
(c) 248 000
(f) 0.321
6. Convert the following. Express your final answer in scientific notation
(a) 239 mm =
m
(d) 38 kg =
mg
(b) 38 L =
mL
(e) 2.2 km =
cm
(c) 561 mg =
g
(f) 2.65 MJ =
J