Math 121 Review. If I only knew ab SUM a + b DIFFERENCE a-b PRODUCT ab 47 -47 4-7 -4-7.
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Transcript of Math 121 Review. If I only knew ab SUM a + b DIFFERENCE a-b PRODUCT ab 47 -47 4-7 -4-7.
Math 121Review
If I only knew…
a b SUMa + b
DIFFERENCEa-b
PRODUCTab
QUOTIENT B TO THE A POWER
4 7
-4 7
4 -7
-4 -7
Did you know???
• Did you know???????• You can never... actually reach the end of a rainbow, where a
pot of gold supposedly awaits. As you move, the rainbow that your eyes see moves as well, because the raindrops are at different spots in the atmosphere. The rainbow, then, will always "move away" at the same rate that you are moving.
Tobey & Slater, Beginning Algebra, 7e 5© 2010 Pearson Prentice Hall. All rights reserved.
Multiplying PolynomialsUse the distributive property to multiply a monomial by a polynomial.
Example:a.) Multiply. 3(c – 4)
3(c – 4) = 3(c) + 3(– 4)
= 3c – 12
b.) Multiply. 2x3(x2 – x + 2)
2x3(x2 – x + 2) = 2x3(x2) + 2x3(– x) + 2x3(2)
= 2x5 – 2x4 + 4x3
Tobey & Slater, Beginning Algebra, 7e 6© 2010 Pearson Prentice Hall. All rights reserved.
The FOIL MethodExample: Multiply using the FOIL method.
(7x + 3)(2x + 4)
= (7x)(2x)
(7x + 3)(2x + 4)
F
F
O
O+ (7x)(4) + (3)(2x)
I
I+ (3)(4)
L
L
= 14x 2 + 28x + 6x + 12= 14x 2 + 34x + 12
Tobey & Slater, Beginning Algebra, 7e 7© 2010 Pearson Prentice Hall. All rights reserved.
Scientific notation is the way that scientists easily handle very large numbers or very small numbers.
Tobey & Slater, Beginning Algebra, 7e 8© 2010 Pearson Prentice Hall. All rights reserved.
Scientific Notation
Scientific Notation A number is written in scientific notation if it is in the form a × 10n, where 1 a 10 and n is an integer.
8200 = 8.2 1000 = 8.2 103
Greater than 1 and less than 10
Power of 10
34,200,000 = 3.42 10000000 = 3.42 107
Scientific notation
Tobey & Slater, Beginning Algebra, 7e 9© 2010 Pearson Prentice Hall. All rights reserved.
Decimal Notation to Scientific Notation
Example: Write 67,300 in scientific notation.
67,300. = 6.73 10n
Starting position of decimal point
Ending position of decimal point
What power?
The decimal point was moved 4 places to the left, so we use a power of 4.
67,300 = 6.73 104
A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.
Tobey & Slater, Beginning Algebra, 7e 10© 2010 Pearson Prentice Hall. All rights reserved.
Example: Write 0.048 in scientific notation.
0.048 = 4.8 10n
Starting position of decimal point
Ending position of decimal point
What power?
The decimal point was moved 2 places to the right, so we use a power of –2.
0.048 = 4.8 10–2
A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10.
Decimal Notation to Scientific Notation
Tobey & Slater, Beginning Algebra, 7e 11© 2010 Pearson Prentice Hall. All rights reserved.
Scientific Notation to Decimal Notation
Example: Write 9.1 104 in decimal notation.
9.1 104 = 9.1000 104 = 91,000
Move the decimal point 4 places to the right.
Example: Write 6.72 10–3 in decimal notation.
6.72 10–3 = 6.72 10–3 = 0.00672
Move the decimal point 3 places to the left.