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!
What’s on the Menu?
Powers and Exponents
Powers
Powers or exponents are used to write down in a short way the multiplication of a
number with itself over and over again.
Exponent – the number of times you are multiplying
6
3
the base number times itself
Base – the number you are multiplying
The Power…
What it Says…
What it Means…
And the answer is…
34
3 to the power of 4
3x3x3x3=
81
53
5 to the power of 3
125
98
9 to the power of 8
5x5x5=
9x9x9x9x9x9x
9x9=
A really BIG number
The last example 98 is too large to figure out using paper/pencil or mental math.
We can use a calculator for these examples.
x
On the calculator find the y button.
x
Press 9, y then, then 8, and finally ENTER.
What is your answer?
The Power Trick
Any base raised to the power of 0 (except 0) equals 1.
20 = 1
30 = 1
80 = 1
How is this possible?
Many people think that any number raised to the 0 power is 0.
But when working with exponents/powers, the number pattern should show a constant
multiplication of your base number.
Number
Pattern
Number
Pattern
Number
Pattern
20
1
x2
30
1
x3
80
x8
21
2
x2
31
3
x3
81
x8
22
4
x2
32
x3
82
x8
23
x2
33
x3
83
x8
24
x2
34
x3
84
x8
Understanding Exponents in Base 10
Base 10 Table
Find the patterns (There are two!)
101
= 10
10-1
= .1
102
= 100
10-2
= .01
103
= 1000
10-3
= .001
104
= 10000
10-4
= .0001
105
= 100000
10-5
= .00001
106
= 1000000
10-6
= .000001
What are the patterns in the table above?
Multiply:
3 x 104
1) 3 can be re-written as 3. (with a decimal on the end)
2) The exponent +4 tells you how many times to move your decimal to the right
3) Fill in the empty spaces with zeros
3. "30,000.
Multiply:
7.2 x 10-3
1) 7.2 already has a decimal
2) The exponent -3 tells you how many times to move your decimal to the left
3) Fill in the empty spaces with zeros
!
.0072 " 7.2
Steps To Success:
1) Re-write your number with the decimal at the end (if it doesn’t already have one in the
number)
2) Determine if you will move right (+ exponent) or left (– exponent)
3) Fill in the empty spaces with zeros
!
Science and Math: What a Pair
Scientific Notation
Scientific notation is a way to express numbers using
powers of 10. It comes in handy when talking about
very BIG or very small numbers.
Numbers in scientific notation include three numbers:
a coefficient, a base number, and an exponent.
5.43 x 106 exponent
coefficient
base
Powers of 10
101 = 10
102 = 100
103 = 1000
104 = 10000
10-1 = 0.1
10-2 = 0.01
10-3 = 0.001
10-4 = 0.0001
To change a number from Scientific Form to Standard Form
The
Scientific
Number
Expanded Form of
Power of 10
3.4 x 107
107 = 10,000,000
Multiply coefficient
by the expanded
Power of 10
3.4 x 10,000,000
5.601 x 109 109 = 1,000,000,000 5.601 x 1,000,000,000
7.5 x 105
105 = 100,000
8.23 x 103
103 =
7.5 x
“Move It to
Multiply It”
Answer
3.4 → 34,000,000.
34,000,000
Move the decimal 7 times
5.601 → 5,601,000,000
Move the decimal 9 times
7.5 → 750,000.
Move the decimal ________
8.23 →
To write numbers in scientific notation remember the following:
1) The coefficient must be a number less than 10 and greater than 1
12,000 → 1.2
4,400 → 4.4
987,000 → 9.87
130 → _______
5,600 → _______
63,230 → _______
2) The base must always be the number 10
Simple Enough!
3) The exponent represents the movement of the decimal point in the
number
34,000. → 3.4000
It was moved 4 times
Use 104
560. → 5.60
It was moved 2 times
Use 102
.0035 → 003.5
It was moved 3 times
Use 103
Change a number from Standard Form to Scientific Form
The
Standard
Number
5,300.
12,830,000.
45,000.
625.
874,000.
The
coefficient
has to be
between 1
and 10
5.300
Move the decimal
point
1.2830000
Move the decimal
point
The base
number
must be a 10
The
movement of
the decimal
10
3 times
10
7 times
10
PUT IT
TOGETHER
5.3 x 103
Drop the unnecessary
zeros
7
1.283 x 10
Drop the unnecessary
zeros
4.5 x 104
6.25 x 102