Unit 4 Factors, Fractions, Exponents and Scientific Notation

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Unit 4Factors, Fractions, Exponents and
Scientific Notation

• Heading

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Prime Number Composite Number
A whole number greater than one that has only two
DISTINCT factors, 1 and itself.
SPECIAL NOTE 1 is neither prime not
composite !!!
A whole number greater than one that has more
than two DISTINCT factors.
Cross out composite numbers. Circle prime
numbers. 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46
47 48 49 50
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Divisibility Rules 2 3 4 5 6 9 10
even
Ends in 0 or 5
Ends in zero
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Determine if the following are divisible by 2, 3,
4, 5, 6, 9, or 10. 1. 3. 5. 2. 4. 6. PRIM
E FACTORIZATION and relatively prime
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Equivalent Fractions A ONE IN DISGUISE
is To make equivalent (equal)
fractions 1. 3. 5. 2. 4. 6.

Any number divided by itself (or over itself)
Examples
Multiply by a ONE IN DISGUISE!
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Reduce Fractions These mean the same thing
Reduce Simplify Write in Lowest
Terms To reduce fractions 7. 9. 11.
8. 10. 12.
Divide by a ONE IN DISGUISE!
This may take more than one step unless you can
find the GCF!
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Change Improper Fractions to Mixed
Numbers Step 1 Step
2 1.
3. 2. 4.
Divide
Remainder forms a fraction
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Change Mixed Numbers to Improper Fractions Step
1 Step 2 5. 7. 6.
8.
Whole number x denominator numerator equals
your new NUMERATOR!
Keep the same DENOMINATOR!
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Rational Numbers Show that the
following are rational numbers.
1. 3. 2. 4. Write
fractions and mixed numbers as decimals Write
decimals as rationals (fractions) 5. 8. 11.
14. 6. 9. 12. 15. 7. 10. 13. 16.
Any number that can be written as the quotient of
two integers . . . In other words .
. . a FRACTION!
Say the decimal properly. Write the fraction,
then simplify.
DIVIDE! Thats what a fraction bar means!
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repeating decimals 0.3737
terminating decimals will happen with
powers of ten multiples of 2, or multiples
of 5
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Exponents (base 10) Decimals Fractions ZERO
EXPONENT a0 Zero Power ? NEGATIVE
EXPONENT a-n Negative Power ? Think
of
Sending the factor with a negative exponent. If
its on the top, send it ______! If its on the
bottom, send it ____!
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1. 4. 7. 10. 2.
5. 8. 11. 3. 6.
9. 12. 13. 14. 15.

• Which is equivalent to 100 0 ?
• 0
• 1
• 10
• 1000

• Which expression is equivalent to 9 -4 ?
• 1/9 4
• 4/9
• -9 4
• -4 9

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POWER OF A POWER PROPERTY Example What to
do 8. 9. 10.
PRODUCT OF POWERS PROPERTY Example What to
do 1. 2. 3.
POWER OF A PRODUCT PROPERTY Example What
to do 15. 16.
SHORTCUT!
Write out factors in expanded form. Simplify
using exponents.
MULTIPLY exponents. Simplify if necessary.
Find the power of each factor and multiply.
It works like distributing!
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4. 11. 17. 5. 12. 18. 1
3. 6. 19. 7. 14. 20.
Which expression is equivalent to (y-3)3
? A) B) C)
D) 1
Simplify the expression (2x3)4. A) 2x7 C)
8x3 B) 2x12 D) 16x12
Which is an equivalent expression to
? A) x2 C) x12 B) x-2 D) x-12
Which value of N would make the statement
true? A) N -6 C) N -14 B) N -10 D)
N -24
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QUOTIENT OF POWERS PROPERTY Example What to
do 1. 2. 3.
POWER OF A QUOTIENT PROPERTY Example What to
do 9. 10.
Write out factors in expanded form. Simplify by
canceling out common factors.
Find the power of the numerator and the power of
the denominator and divide.
It works like distributing!
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4. 11. 16. 5. 12. 6. 13.
17. 7. 14. 8. 15
.
Which expression is equivalent to 108? A) B)
C) D)
Which is an equivalent form of the fraction
? A) B) C) D)
Which is equivalent to ? A)
B) C) D)
Evaluate . A) -27 B) 27 C) D)
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Scientific Notation Examples NOTE!!
The SHORTCUT involves The EXPONENT
MEANS Keep in mind the concept of Rewrite
in Standard Notation. Rewrite in Scientific
Notation 1. 8. 2. 9. 3. 10. 4.
11. 5. 12. 6. Cruising speed of a
supersonic jet is 1.33 x 103 miles per hour.
13. The population of Asia in 2011 was
about 3,271,000,000. 7. One wolffia plant has
a mass of about 1.5 x 10-4 gram. 14.
It takes 0.000000000334 seconds for light to
travel one meter.
A method of writing very large or very small
numbers. It is written as a number between
one and ten times a power of ten.
ZINGS of the decimal.
ZINGS, not zeroes.
positive exponents being BIG numbers
negative exponents being SMALL numbers
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Scientific Notation ADVANCED Compare using lt , gt
, or . (HINT! Write all in standard OR all
in scientific notation if necessary) 1. 2.
Order from least to greatest. (HINT! Write
all in standard OR all in scientific notation if
necessary) 3. How many times larger is one
number than another? (HINT! Write all in
standard notation first) 4. How much larger is 9
x 105 compared to 3 x 103 ? 5. 6 x 105 is how
many times as great as 3 x 102 ? A) 2
times C) 200 times B) 20 times D) 2000
times 6. Your friend thinks that 4 x 103 is
twice as great as 2 x 102. What error is your
friend making? Explain your reasoning.