10/3/11 5.1 Integer Exponents and Scientific
Notation
•  Use the rules of exponents to simplify expressions.
•  Rewrite exponential expressions involving negative and
zero exponents.
•  Use scientific notation to write very large and very small
numbers.
Rules of Exponents
1 10/3/11 Rules of Exponents
Rules of Exponents
2 10/3/11 Few examples
Scientific Notation
3 10/3/11 Uses – scientific notation
•  Earth’s mass is
5 980 000 000 000 000 000 000 000
= 5.98 ⋅1024
Any number can be written as a product of a number
between 1 and 10 and a power of 10
Write in scientific notation
•  346=
•  73450=
•  874300=
•  659000000=
•  22=
•  7.3=
•  0.75=
•  0.0043=
•  0.0000328=
•  0.0000000092=
4 10/3/11 Interesting tidbits?
Value
Value Expanded
Short Scale
10 0
=
10 3 =
10 6 =
1 one
1,000 thousand
1,000,000 million
10 9 =
1,000,000,000 billion
1012 =
1,000,000,000,000 trillion
1015 =
1,000,000,000,000,000 quadrillion
1018 =
1021 =
1024 =
1,000,000,000,000,000,000 quintillion
1,000,000,000,000,000,000,000 sextillion
1,000,000,000,000,000,000,000,000 septillion
Long Scale
one
thousand
million
thousand million
(sometimes milliard)
billion
thousand billion
(sometimes billiard)
trillion
thousand trillion
(sometimes trilliard)
one quadrillion
Example problem
•  Did you notice we live in times of economic turmoil? The
proposed Wall Street bailout plan is requesting Congress
to dish out $700 billion to help large banks live through the
hard times they have created. If the US has 300 million
people, how much money is that per person? However,
not every baby can contribute that much. If we only
consider the taxpayers in the US, and there are 1.4·108 of
them, then we find that that is 114% more than the
amount you just found. How much per taxpayer will this
bill cost?
5 10/3/11 5.2 Addition/Subtraction of Polynomials
•  Identify leading coefficients and degrees of polynomials.
•  Add and subtract polynomials.
Polynomials
A Polynomial in x is an expression of the form:
an x n + an −1 x n −1 + ...+ a2 x 2 + a1 x + a0
where an ≠ 0 and n is a nonnegative integer.
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6 10/3/11 Give an example of:
•  Monomial of degree 0
•  A trinomial of degree 5 and with constant term 3
•  A binomial of degree 2 and leading coefficient -2
Add/Subtract Polynomials
7 10/3/11 Adding and subtracting polynomials
5.3 Multiply Polynomials
•  Use the distributive Property and the FOIL method to
multiply polynomials.
•  Use special product formulas to multiply binomials.
8 10/3/11 Garden problem
I want to put a fence around my garden to keep the dogs
out. To make it easy on myself I’ll make it rectangular, so
that one side 14 yards long. I bought 60 yards of lattice
fence. However, I want to use at least 50 yards of my
fence, otherwise the garden would be too small. What
should be the width of my garden?
Area of a square?
•  This square has side a cm. What is its area?
9 10/3/11 Area of a different square:
•  (x+3)2 must be the area of a square whose side is x+3
Multiplying Polynomials
The key to multiplying polynomials is the DISTRIBUTIVE
PROPERTY.
10 10/3/11 Multiplying polynomials
One more multiplication
11 10/3/11 Special Products
Volume
•  A closed rectangular box has sides of lengths n,
n+2 and n+4 inches.
•  Write a polynomial function V(n) that
represents the volume of the box.
•  What is the volume of the box if the
length of the shortest side is 2 inches?
•  Write a polynomial function A(n) that
represents the area of the base of the box.
•  Write a polynomial function for the area of the
base if the lengths and width increase by 4.
12