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Transcript
Math 8 Unit 2 Exponents
Fall 2007
References
Helpful Links:
http://www.pbs.org/wg
bh/nova/proof/puzzle/t
heorem.html
http://www.purplemath
.com/modules/translat
2.htm
http://www.aplusmath.
com/Flashcards/sqrt.ht
ml
http://www.math.com/
school/subject1/lessons
/S1U1L9GL.html
http://www.arcytech.or
g/java/pythagoras/
Volume 1 Issue 2
Dear Parents
Below you will find a list of concepts that your child will use and understand while
completing Unit 2 Exponents. Also included are references, vocabulary and examples
that will help you assist your child at home.
Concepts Students will Use and Understand





An irrational number is a real number that can not be written as a ratio of two
integers.
All real numbers can be plotted on a number line.
Exponents are useful for representing very large or very small numbers.
Square roots can be rational or irrational.
Some properties of real numbers hold for all irrational numbers.
Vocabulary
Additive Inverse: The sum of a number and its additive inverse is zero. Also called the
opposite of a number. Example: 5 and -5 are additive inverses of each other.
Exponent: The number of times a base is used as a factor of repeated multiplication.
Exponential Notation: See Scientific Notation below.
Mathematics Course 3
Textbook Connection:
Chapter 4: Lessons 1-8
Mathematics Course 3
Textbook Online:
http://go.hrw.com/reso
urces/go_mt/hm3/so/c
3ch4aso.pdf
http://go.hrw.com/reso
urces/go_mt/hm3/so/c
3ch4bso.pdf
Hypotenuse: The side opposite to the right angle in a right triangle.
Irrational: A real number whose decimal form is non-terminating and non-repeating that
cannot be written as the ratio of two integers.
Leg: Either of the two shorter sides of a right triangle. The two legs form the right angle of the
triangle.
Pythagorean Theorem: A theorem that relates the lengths of the sides of a right triangle:
The sum of the squares of the lengths of the legs of a right triangle equals the square of the
length of the hypotenuse.
Radical: A symbol that is used to indicate square roots.
Rational: A number that can be written as the ratio of two integers with a nonzero
denominator.
Scientific Notation: A representation of real numbers as the product of a number between 1
and 10 and a power of 10, used primarily for very large or very small numbers.
Significant Digits: A way of describing how precisely a number is written.
Square root: One of two equal factors of a nonnegative number. For example, 5 is a square
root of 25 because 5•5 = 25. Another square root of 25 is -5 because (-5)•(-5) = 25. The +5
is called the principle
Math 8 Unit 2 Exponents Practice Problems
Example 1
1. Write the following expressions in exponent form:
a.
c c c c c
b.
1
100
4
3
2
2. Write in fraction form
7a b y
3. Change to standard form: 8.51 x 10-2
4. Change to scientific notation: 107,000,000,000
Example 2
5. Find the following square roots, graph the results on a number line and explain why each result is
rational or irrational:
a.
144
56
b.
6. Estimate the square root of 18.
7. What are the two square roots of 36?
8. Simplify the following expression:
5
2 6
4
Example 3
Use the Pythagorean Theorem to solve:
9. a= 4 and b=6, then what does c equal?
10. If the square of the hypotenuse is equal to 100 and a leg is equal to 6, then what is the length of the
other leg?
11. Solve for the unknown variable:
13cm
5cm
x
Answer Key
Example 1
1 a. c 5
Example 3
5
8. 2 3 
2
9. about 7.2
b. 102
7b3
2. 4 2
10. 8
a y
3. 0.0851
11. 12cm
4. 1.07  1011
Example 2
5. a. 12, rational because it can be written as a ratio.
b. about 7.48, irrational because the exact value is a non-terminating, non-repeating decimal.
6. Between 4 and 5; closer to 4; about 4.2
7. 6