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Math Skills
• In this chapter we will review basic skills
necessary to perform mathematical
calculations in physics, these include
• Signed Numbers
• Metric System conversions
• Significant Figures
• Scientific Notation
Signed Numbers
• Addition Rule: To add two numbers of like
sign, we add the absolute values of the
numbers and give the sum the common sign.
To add two numbers of unlike sign, we find
the difference of their absolute values and
give the result the sign of the larger value.
• (+6) + (+2) = +8
• (+6) + (-2) = + 4
Signed Numbers
• To subtract one signed number b from
another signed number a, we change the sign
of b and then add it to a, using the addition
rule.
• (+8) - (+5) = 3
• (-8) – (+5) = -13
Signed Numbers
• Multiplication Rule: If two factors have like
signs, their product is positive. If two factors
have unlike signs, their product is negative
• (+2)(+3) = +6
(-3)(-4) = +12
• (-2)(+3) = -6
(-3) (+4) = -12
Signed Numbers
• Division Rule: The quotient of two numbers of
like sign is positive, and the quotient of two
numbers of unlike sign is negative.
• (+2) ÷ (+2) = +1 (-4) ÷(-2) = +2
• (+4)÷ (-2) = -2
(-4) ÷ (+2) = -2
Quadratic Equations
• For mathematical expressions involving a
second order term, arrange the equation to
identify a, b, and c.
• ax2 + bx + c = 0
• Two solutions will be obtained from the
quadratic equation
 b  b 2  4ac
x
2a
Metric System
• The Metric System is a set of standards that is
widely adopted to make measurements
meaningful
• We will consider standards for length, time,
and mass
Metric System
• The mass
standard is a
platinum/iridium
cylinder kept
under vacuum.
Metric System
The atomic clock is based on
vibrations of the Cesium atom.
One second is the time
needed for 9,192,631,770
vibrations of the Cesium atom.
Metric System
• The standard of length is based on the
distance light travels in a certain period of
time. One meter is the length of path traveled
in a vacuum in a time interval of
1/299,792,458 seconds.
Metric System Prefixes
Prefix
Multiple
Symbol
Pico
10-12
p
Nano
10-9
n
micro
10-6
µ
milli
10-3
m
Prefix
centi
Multiple
10
-2
Symbol
c
Kilo
103
K
Mega
106
M
Giga
109
G
Derived Units
• Derived units are mathematical combinations
of the basic units.
• Example #1 velocity: meters/second
• Velocity has units of length/ time
• Example #2: area: meters2
• Area is length x length
Significant Figures
•
•
•
•
The following are always significant:
All nonzero digits
All zeroes between nonzero digits
Zeroes to the right of an non-zero digit and left of a written decimal
point
• Zeroes to the right of a non-zero digit and right of a written decimal
point
• The following are never significant
• Zeroes to the right of a nonzero digit, but to the left of an unwritten
decimal point
• Zeroes to the left of the decimal point in numbers less than one.
• Zeroes to the right of a decimal point, but to the left of the first
non-zero digit
Adding Significant Figures
• When adding or subtracting using significant
figures- express your answer to the same digit
as the least accurate term.
• Examples
• 1.18 + .00037 + .261 =
• 24.686 + 2.343 + 3.2 =
Multiplying and Dividing Significant
Figures
• Complete the operation your problem
specifies. Count the number of significant
figures in each term. The answer is expressed
to the smallest number of significant figures in
any term.
• Examples
• 1.4 x 5.632 =
• 618/50 =
Scientific Notation
• Scientific Notation is a shorthand used to
express large and small numbers.
• In scientific notation we our value as a
number between 1 and 10 times an integral
power of 10.
• 0.000021 becomes 2.1 x 10-5
• 3,450,000 becomes 3.45 x 106
Arithmetic Operations in Scientific
Notation
•
•
•
•
•
•
•
•
Adding and subtracting with like exponents
4 x 108 + 3 x 108 =
Adding and subtracting unlike exponents
4.0 x 106 + 3.0 X105 =
Multiplication
(3 x 106 m) (2 x 103 m) =
Division
8 x 106m/ 2 x103 s =