Name: _________________________
Date: _____________________
The Metric System
• The metric system is based on multiples of 10. Each type of measurement (length, mass, volume,
energy, and so on) has a base unit. Larger and smaller units are named by adding a prefix to the base
unit.
• For example, the basic unit of mass is the gram. The prefix kilo- means multiplied by 1000, so one
kilogram is 1000 grams. The prefix milli- means divided by 1000, so one milligram is one thousandth of
a gram.
• The table shows the most commonly used metric prefixes.
Prefix
Symbol
Relationship to the Base Unit
giga-
G
109 = 1 000 000 000
mega-
M
106 = 1 000 000
kilo-
k
103 = 1000
hecto-
h
102 = 100
deca-
da
101 = 10
100 = 1
deci-
d
10-1 = 0.1
centi-
c
10-2 = 0.01
milli-
m
10-3 = 0.001
micro-

10-6 = 0.000 001
nano-
n
10-9 = 0.000 000 001
 The table shows some basic units for measurements commonly used in science.
Basic Units for Measurements Commonly Used in Science
Measurement
Base Unit
Symbol
Mass
gram
g
Volume
litre
L
Length
metre
m
Energy
Joule
J
Power
Watt
W
Introduction to Physics – Metric Conversions and Scientific Notation
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Name: _________________________
Date: _____________________
Converting Metric Units Using Conversion Factors
• You can use conversion factors to convert metric units. To determine the conversion factor you can
use metric stairs. To use the stairs, simply start at the level of the original unit (litre, metre, gram) and
move up or down the stairs to the unit to which you are converting. Each "jump" up the stairs
increases the conversion factor by a power of 10
• Example 1: To convert 3.4 cm to metres, make two jumps up the stairs. The conversion factor will
be 10 x 10 cm = 1 m, or 100 cm = 1 m. To convert the measurement, multiply the value by the
conversion factor. Make sure that when you write the conversion factor, the unit you want to cancel
is on the bottom of the conversion factor:
3.4 cm x
1m
100 cm
= 0.034 𝑚
• Example 2: Convert 5.2 km to metres. There are 3 jumps on the stairs between km and m. The
conversion factor is 10 x 10 x 10 m = 1 km, or 1000 m = 1 km. To convert the measurement, multiply
the value by the conversion factor. Note that the km unit is written on the bottom of the conversion
factor because that is the unit you want to cancel.
5.2 𝑘𝑚 𝑥
1000 𝑚
1 𝑘𝑚
= 5200 𝑚
Introduction to Physics – Metric Conversions and Scientific Notation
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Name: _________________________
Date: _____________________
Questions – Complete the two examples, then do the conversion questions.
Example 3 - Convert 65 mm to metres.
Solution - Look at the stairs on the previous page. To convert millimetres to metres, jump up three
stairs. The conversion factor is 1000 mm = 1 m.
65 mm =
Example 4 - Convert 13 km to metres.
Solution - Look at the stairs on the previous page. To convert kilometres to metres, jump down three
stairs. The conversion factor is 1000 m = 1 km.
13 km =
Convert each value to the given measurement.
1. 160 km = ___________ m
2. 0.16 g = ____________ mg
3. 1.6 cL = _______________ L
4. 16 000 cm = ____________ m
5.
6.
7.
8.
0.16 kg = ______________ g
9.21 MJ = ______________ J
0.921 kg = ______________ g
92.1 nm = ______________ m
Writing Scientific Notation
Scientific notation is a way of writing very large or very small numbers so they are easier to work with.
A number written in scientific notation is the product of a number between 1 and 9, and a power of 10.
Large numbers have a power of 10 with a positive exponent. Small numbers have a power of 10 with a
negative exponent.
Example 1
The diameter of the Sun is about 1 400 000 km. Write 1 400 000 in scientific notation.
Solution
The number will have two parts: the first digit of the number, a decimal place followed by the remaining
digits (except trailing zeros, unless they are significant) and a power of 10. The first number will be 1.4.
What do you need to multiply 1.4 by to get 1 400 000?
1 400 000 = 1.4  1 000 000
= 1.4  106
Write 1 000 000 as a power of 10.
Check: Move the decimal in 1.4 six places to the right and you get 1 400 000.
Introduction to Physics – Metric Conversions and Scientific Notation
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Name: _________________________
Date: _____________________
Example 2
The radius of a carbon atom is 0.000 000 000 077 m. Write 0.000 000 000 077 in scientific notation.
Solution
The first number will be 7.7. What do you need to multiply 7.7 by to get 0.000 000 000 077?
0.000 000 000 077 = 7.7  0.000 000 000 01
Write 0.000 000 000 01 as a power of 10.
= 7.7  10–11
Check: Move the decimal in 7.7 eleven places to the left and you get 0.000 000 000 077.
Express each of the following in scientific notation.
1. 2350 g of sulfuric acid are released when a certain amount of coal is burned. ______________
2. The average person is exposed to up to 300 millirems of radiation per year. ______________
3. The mass of a proton in a hydrogen atom is 0.000 000 000 000 000 000 000 000 001 673 kg.
______________
3
4. The density of the Sun’s lower atmosphere is 0.000000028 g/cm .
______________
Calculating with Scientific Notation
You can multiply and divide with numbers in scientific notation without needing to write them in
standard form. Use the exponent laws to calculate the new power of 10.
Product of Powers: am  an = am + n
Quotient of Powers: am ÷ an = am – n
Example 1
Convert 9.7  107 AU to light years. Conversion factor: 1 AU = 1.58  10–5 light years
Solution
If you are multiplying powers with the same base, you can add the exponents.
9.7 𝑥 107 𝐴𝑈 𝑥
1.58 𝑥 10−5 𝑙𝑖𝑔ℎ𝑡 𝑦𝑒𝑎𝑟𝑠
𝐴𝑈
= 9.7 𝑥 1.58 𝑥 107 𝑥10−5 𝑙𝑖𝑔ℎ𝑡 𝑦𝑒𝑎𝑟𝑠
= 15.326 𝑥 107+(−5) 𝑙𝑖𝑔ℎ𝑡 𝑦𝑒𝑎𝑟𝑠
= 15.326 𝑥 102 𝑙𝑖𝑔ℎ𝑡 𝑦𝑒𝑎𝑟𝑠
Check: The first number is not between 1 and 10. Change the number to proper scientific notation.
15.326  102 = 1.5326  103 light years
Introduction to Physics – Metric Conversions and Scientific Notation
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Name: _________________________
Date: _____________________
Example 2
Convert 2.1  108 light years to astronomical units. Conversion factor: 1 AU = 1.58  10–5 ly
Solution
If you are dividing powers with the same base, subtract the exponents.
2.1 𝑥 108 𝑙𝑦 𝑥
1 𝐴𝑈
1.58 𝑥 10−5 𝑙𝑦
2.1 𝑥 108
=
𝐴𝑈
1.58 𝑥 10−5
= 1.329 𝑥 108−(−5) 𝐴𝑈
= 1.329 𝑥 1013 𝐴𝑈
Check: The first number is between 1 and 10 and the second number is a power of 10, so the number is
written in proper scientific notation.
Solve the following. Express your answers in proper scientific notation.
1. (5.75  109)  (1.4  102)
3.
2. (2.6  104)  (3.5  103)
4.
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