Download Exponents and Powers of Ten.notebook

Exponents and Powers of Ten.notebook
Exponents and Powers of Ten
October 07, 2015
Lesson 1: Exponents
Jul 30­8:42 AM
Jul 30­8:44 AM
Exponents
Base
Number
8
2
Exponent - written as a small
number to the right and above
the base number
The exponent tells the number of times you multiply the base number by
itself.
20 = 1
21 = 2
22 = 2 x 2
23 = 2 x 2 x 2
24 =
25 =
26 =
**ANY NUMBER
WITH AN
EXPONENT OF
ZERO IS EQUAL
TO ONE**
50 = 1
51 = 2
52 = 2 x 2
53 = 2 x 2 x 2
54 =
55 =
56 =
Exponents Practice
In your notes, copy the chart and fill in the missing pieces.
Exponential
Number
Meaning
How to Say It
32
6 x 6 x 6 x 6
• seven to the third power
EX: 40 = 1
• the third power of seven
You can read exponential numbers several different ways.
• seven cubed
_________ to the _________ power
base number
exponent as a cardinal number
47
The _________ power of __________.
exponent as a cardinal number
base number
If the exponent is 2, you can say ________ squared.
base number
• nine to the fifth power
• the fifth power of nine
If the exponent is 3, you can say ________ cubed.
base number
Jul 30­8:44 AM
Jul 30­8:44 AM
Exponents and Your Calculator
To type in an exponential
number, you need to:
Lesson 2: 1. Key in base number
2. Press caret symbol
3. Key in exponent
4. Press enter
Click the link to the
right to see a
demonstration.
http://www.showme.com/sh/?h=grXYRoO
Jul 30­8:44 AM
Powers of Ten
Jul 30­8:44 AM
1
Exponents and Powers of Ten.notebook
October 07, 2015
Powers of Ten
Powers of Ten
When we say "powers of ten" we are talking about the number 10 as the base
number raised to different powers, or in other words, 10 with different
exponents. Before you start, remember that any number to the power of zero
always has a value of one. (ex. 100 = 1)
Questions to consider:
1. What happens to a whole number when you multiply it by 10 ( or 101 )? Try it
on your calculator.
Value
Power of Ten
Expression
101
10
10
102
10 x 10
100
2. What happens to a whole number when you multiply it by 100 ( or 102 )?
103
3. Fill in the missing pieces in the chart below. Use your calculator to find the
value of the expressions.
104
105
106
Expression
107
7 x 102
108
8 x 104
10
35 x 103
9
Notice that the exponent of each 10
matches the number of zeros that the
value has.
Value
What do you notice about what happens when you multiply a whole number
by a power of ten? Could this be done easily without a calculator?
If I give you the value 34,000, can you tell me the expression that was
used? Think about the number of zeros that have been added.
Jul 30­8:44 AM
Jul 30­8:44 AM
Powers of Ten
In the last lesson, you added zeros to whole numbers when you multiplied
them by powers of ten by looking at the exponents. For example, if you has
3 x 107, you added seven zeros to the 3 to get a value of 30,000,000.
Lesson 3: Multiplying by Powers of Ten
Instead of thinking that you are adding zeros, let's refer to what is
happening another way. Every whole number has a decimal. It is not used
unless you are adding fractional amounts to it. For example, think of the
number 3 like this:
3.
When you multiply this 3 by a power of ten, you are not actually adding zeros.
You are actually moving your decimal to the right the number of times the
exponent tells you to.
3 x 107 = 3.0000000.
Jul 30­8:44 AM
Powers of Ten
With this knowledge, we can multiply decimal numbers by powers of ten as
well. Find the values of the following expressions with your calculator. Write
down the expressions and their values in your notes.
Jul 30­8:44 AM
Multiplying by 0.1, 0.01, and 0.001
You can also use this pattern to multiply numbers by the decimals 0.1, 0.01,
and 0.001. When you multiply a number by a number less than one, you are
only taking a part of that number rather than making the number larger.
Try the following expressions on your calculator.
1. 3.637 x 10
345 x 0.1
2. 3.637 x 102
3. 3.637 x 103
345 x 0.01
4. 9.2 x 10
345 x 0.001
5. 9.2 x 102
6. 9.2 x 104
What did you notice? What happened to the decimal in the original number
each time? Did the decimal move the same way as it does when you multiply
by powers of ten?
Jul 30­3:58 PM
Jul 30­3:58 PM
2
Exponents and Powers of Ten.notebook
October 07, 2015
Lesson 4: Dividing by Powers of Ten
Recall that when you multiply by powers of ten, you move the decimal to the
RIGHT the number of times indicated by the exponent on the ten. This makes
your answer larger than your first number.
Dividing by Powers of Ten
3 x 107 = 3.0000000.
What do you think happens to the decimal when you divide by a power or ten?
How are multiplication and division related?
Multiplication and division are opposites. Multiplying whole numbers
makes them larger and dividing whole numbers makes them smaller.
When you divide by a power of ten, the decimal will move to the
LEFT instead of the right, making the original number smaller.
Jul 30­3:58 PM
Jul 30­3:58 PM
Dividing by 0.1, 0.01, and 0.001
Dividing by Powers of Ten
Try these on your calculator. Notice what happens to the decimal on
each. Compare these answers to the ones on the last lesson's practice
problems.
You can also use this pattern to divide numbers by the decimals 0.1, 0.01,
and 0.001. When you divide a number by a number less than one, it is like
multiplying because your answer will be larger. Try the following expressions
on your calculator.
1. 3.637 ÷ 10
345 ÷ 0.1
2. 3.637 ÷ 102
345 ÷ 0.01
3. 3.637 ÷ 103
4. 9.2 ÷ 10
345 ÷ 0.001
5. 9.2 ÷ 102
What did you notice? What happened to the decimal in the original number
each time? Did the decimal move the same way as it does when you divide by
powers of ten?
6. 9.2 ÷ 104
Aug 3­3:09 PM
Aug 3­3:09 PM
Quick Review
Remember that every number has a decimal. If there is no fractional amount,
the decimal is located to the right of the ones place.
When to move the decimal to the RIGHT (making the number larger):
1. MULTIPLYING by powers of ten
3.637 x 103 = 3,637
2. DIVIDING by 0.1, 0.01, or 0.001
345 ÷ 0.01 = 34,500
When to move the decimal to the LEFT (making the number smaller):
1. DIVIDING by powers of ten
363.7 ÷ 103 = 0.3637
2. MULTIPLYING by 0.1, 0.01, or 0.001
345 x 0.01 = 3.45
Aug 3­3:23 PM
Aug 10­11:51 AM
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