Download 5-1 Day 2 Worksheet

ALGEBRA II
5-1 Day 2 Reading Guide
PART ONE: SCIENTIFIC NOTATION
Scientific notation allows us to express very large numbers and very small numbers in a more “manageable” form.
1.
Change the expression from scientific notation to decimal notation.
a) 100457
Step one: Move decimal over so that there is one place in front of the decimal
1.00457
Step Two: Count how many places you moved over the decimal
We moved the decimal over 5 places to the left…
this is equivalent to 105 or 100000
Step Three: Write in scientific notation
1.00457 x 105
a) .00000457
Step one: Move decimal over so that there is one place in front of the decimal
4.57
Step Two: Count how many places you moved over the decimal
We moved the decimal over 6 places to the right…
this is equivalent to 10-6 or 0.000001
Step Three: Write in scientific notation
4.57 x 10-6
You try:
1) .000000656
2) 154522465
You should have gotten:
1) 6.56 x 10-7
2) 1.55 x 108
Multiplication
(3.6 x 104)(3.1 x 103)
Step one: We have two monomials that we are multiplying together. Multiply
The decimals with the decimals and the 10# with the 10#..
11.16 x 107
Step two: We need to move the decimal over one place to have the product in
scientific notation.
1.116 x 108
You try:
(4.2 x 105)(2.7 x 106)
Did you get 11.34 x 1011 = 1.134 x 1012
Division
3.6 10 
3.110 
4
3
Step one: We have two monomials that we are dividing. Divide the corresponding parts.
1.1612 x 101
Step two: It is already in scientific notation, so we are done!
You try:
 2.6 10 
3.110 
7
3
** Check your answer with Mrs. Rende before moving on.
PART TWO: Monomials
A monomial is an expression that is a number, a variable, or a product of a number and one or
more variables.
Examples of monomials:
-3
t4
z
2 2
ab
3
An expression is NOT a monomial if there is more than one term (ex: 10x2 + 5x), variables in the
denominator (ex:
exponents (ex:
1
), variables under radicals (ex:
x
x ), or variables with negative or rational
x 3 or x1/2 ) .
Which of the following ARE monomials?
a. 3x-2
b. 5x5
e. 6
f.
c. 5x2 + 4x
4
x3
g.
d. –6xy2
x
4
The degree of a monomial is the sum of the exponents of all variables. The degree of a constant
is zero.
A coefficient is the constant term in front of the variables.
Ex: 12g 7 h 4i 3  The coefficient is 12. There are 3 variables: g, h, and i. The exponents on the three
variables are 7, 4, 3, so the degree of the monomial is 7+4+3 or 14
Fill out the chart below.
Monomial
3x
-7a2
-k8r
3ab2
10
Coefficient
**Check your answers with Mrs. Rende before moving on.
Degree
PART THREE: Review problems
Simplify using the properties of exponents.
1)
2)
3
 6 x 2 y 4   x3 y 4 
3) 
4 3   2 3 
 3x y   x y 
2
 3x y  5 xy 
4)
x  y
2
8
3
3
**Have Mrs. Rende check your answers and get your homework!
4
2
Algebra II
5-1 Day 2 Homework
Name: ______________________
Date: ____________ Period: ____
PART 1
Express each number in scientific notation.
1) 4,860,000
2) 525,000,000,000
3) 0.0000000064
4) 0.000369
Evaluate. Express the result in scientific notation.
4
4
5) (3.6 x 10 )(5 x 10 )
-3
-2
6) (4.2 x 10 )(3 x 10 )
8) (3.2 x 10 )
9.6  107
9)
1.5  103
11) 433.7 x 108
12) (4.8x 102)(6.9 x 104)
-3 2
1.62  102
7)
1.8  105
10) (6.8 x 10-5)2
PART II
13.) Which of the following are monomials? (Choose all that apply)
[A] –w2
[B] 3x – 7y
[C]
2x
y3
[D] 5x-7
[E] 2xy3
14.) Name the degree and coefficient of the following monomial: -2x3y
PART III
Simplify
2a 2b3
15.)
14ab4
  3m 2 n 2 

18.) 
  2mn 2 3 


16.)
1
 2 
2
6 x 4 y 4 z
 5x y 
  xy 
2
19.)
x3 y 5  z 2 
4 2
5 3
2
 3r 3 
17.)  2 
 s 
2
2 x5  y 2 
20.) 3  3 
y  2x 
3