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[Timeline]
Grade 7: The Learning Equation Math
11.01 Powers and Exponents
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| Learning
Outcomes: The student will:
Study the pattern for powers of 10.
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| Exponential
Form (Power) |
Expanded
Form/Repeated Multiplication |
Standard
Name |
| 106 |
10x10x10x10x10x10 |
1000000 |
| 105 |
10x10x10x10x10 |
100000 |
| 104 |
10x10x10x10 |
10000 |
| 103 |
10x10x10 |
1000 |
| 102 |
10x10 |
100 |
| 101 |
10 |
10 |
| 100 |
1 |
1 |
| 10-1 |
1/10 |
0.1 |
| 10-2 |
1/10 x 1/10 |
0.01 |
| 10-3 |
1/10 x 1/10 x
1/10 |
0.001 |
You can calculate a power on a
scientific calculator. Use this calculator to check the chart above, then try it out
for yourself.
Press Reload/Refresh if the
calculator does not show properly. |
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Review:
| Concept/Term |
Example(s) |
Definition/Explanation |
| power |
81 is the fourth power of 3, because: 3 x 3 x 3 x 3 = 81
34 is another way of writing this power |
the answer from multiplying a number by itself one or more times. A power
has two parts:
baseexponent =
34
and can be written/read in several ways:
- the fourth power of three
- three exponent four
- three to the fourth power
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32
33 |
Exponents 2 and 3 can also be written/read another way:
- 32 is read three squared
- 33 is read three cubed
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| base |
In 34 , the base is 3. |
the number being multiplied in a power |
| exponent |
In 34 , the exponent is 4. |
the number of times a number is being multiplied by itself in a power |
Powers can be expressed in exponential, expanded, or standard from.
| Exponential
Form (Power) |
Expanded
Form/Repeated Multiplication |
Standard
Form (Standard Name) |
34 |
3 x 3 x 3 x 3 |
81 |
33 |
3 x 3 x 3 |
27 |
| 32 |
3 x 3 |
9 |
| 31 |
3 |
3 |
| 30 |
no expanded form |
1 |
Lesson
on Exponents
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Enrichment:
Math
Forum: BEATCALC - tricks for squaring numbers
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expression, power, base, exponent, standard form, factor, squared, cubed
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Prerequisite
Skills:
| multiple |
Repeated addition of a number. Multiples and Common
Multiples - cool
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5, 10, 15, and 20 are multiples of 5. |
| factor |
a number multiplied to produce a product Prime and Composite
Numbers - cool |
1, 2, 3, 4, 6, and 12 are factors of 12. |
| prime |
natural numbers (or positive integers) with exactly two
factors, 1 and itself Prime and Composite
Numbers - cool
Prime and Composite Numbers Practice |
2, 3, 5, 7, 11, 13, 17... |
| composite |
numbers with more than 2 factors. Prime and Composite
Numbers - cool
Prime and Composite Numbers Practice |
4, 6, 8, 9, 10, 12, 14,15, 16, ... |
| neither prime nor composite |
1 has only one factor 0 is not a natural number (or positive
integer) |
0, 1 |
Prime Number Test
source: Prime
Numbers |
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Purpose: Learn to identify the prime numbers. (It may take a few
seconds to start up or reset.)
To eliminate all multiples of 2 (except 2 itself), press 2. Three will not be
eliminated, since it is not a multiple of 2. Press 3 and the Sieve of
Eratosthenes will eliminate all of the multiples of 3 (except 3 itself).
Likewise, to eliminate all multiples of a number (except itself), press its button. Do not
hesitate to experiment. If you follow the directions correctly, the numbers left
will be the prime numbers.
Press the Reset button to start over. You can select a new size (upto
250) for the table by setting the Size: field, and then pressing Reset.
Explaining
the Sieve of Eratosthenes |
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Source: Sieve of Eratosthenes
Prime
Number Generator
Primes |
Magic
Square's Applet
Area
of Rectangles
Area
of a Rectangle Applet
Understanding
Squares of Numbers
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[Timeline]
- Started September, 1998. Copyright © 1999, 2000
 visitors since September 3, 2000
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= baseexponent