Rational Numbers Chapter 1 Lesson 1 Vocabulary Complete
Rational Numbers Chapter 1, Lesson 1
Vocabulary Complete this graphic organizer. Rational Number Define in your own words. Fraction Percent Decimal Mixed Number
Rational Numbers All rational numbers are written as a RATIO. Example 1. During a recent regular season, a Texas Ranger baseball player had 126 hits and was at bat 399 times. Write a fraction in the simplest form to represent the ratio of the number of hits to the number of at bats.
Rational Numbers
Repeating vs. Terminating Decimals Rational Numbers Repeating Decimal Terminating Decimal 0. 50000… 0. 5 0. 40000…. 0. 4 0. 8333… Does not terminate (0. 83)
Example 1 •
Got it? 1 • 0. 75 4. 52 -0. 2 3. 09
Example 2 In a recent season, St. Louis Cardinals first baseman Albert Pujols had 175 hits in 530 at bats. To the nearest thousand, find his batting average. We need to the number of hits, 175 by the number of at bats, 530 175 ÷ 530 = 0. 3301886792 Round to the nearest thousand. 0. 330
Got it? In a recent season, NASCAR driver Jimmie Johnson won 6 of the 36 total races held. To the nearest thousandth, find the part of races he won. Divide the races he won, 6, out of the races he held, 36. 6 ÷ 36 = 0. 1666666… Round to the nearest thousandth. 0. 167
Example 3 •
Example 4 •
Example 5 •
Homework Independent Practice: 1 – 10, 14 – 15, 17, 19
Powers and Exponents Lesson 2
Saving money Yogi decided to start saving money by putting a penny in his piggy bank, then doubling the amount he saves each week. 1. Complete the table. Weekly Savings Total Savings 0 $0. 01 1 $0. 02 $0. 03 2 $0. 04 3 $0. 08 4 $0. 16 $0. 07 $0. 15 $0. 31 5 $0. 32 $0. 63 2. How many 2’s are multiplied to find his savings in Week 4? 4 Week 5? 5 3. How much will he save in Week 8? $2. 56
Write and Evaluate Powers 4 factors 2 2= Power 31 32 33 3 n 4 2 Read and Write Powers Words Factors 3 to the first power 3 3 to the second power 3 3 3 to the third power 3 3 3 3 to the nth power 3 3 … 3 n factors
Example 1 Write each expression using exponents. a. (-2) 3 3 There are three (-2)’s and four 3’s. (-2)3 34 b. a a b b a There are three a’s and two b’s. a 3 b 2
Example 2 •
Example 3 The deck of a skateboard has an area of about 25 7 square inches. What is the area of the skateboard deck? 25 7 2 2 2 7 32 7 224 square inches
Example 4 Evaluate each expression if a = 3 and b = 5. a. a 2 + b 4 32 + 54 9 + 625 = 634 b. (a – b)2 (3 – 5)2 (-2)(-2) = 4
Multiply and Divide Monomials Lesson 3
Monomials Monomial: a number, variable, or a product of a number and variable Examples: 32 74 a 4 b 8 3 x 2 y g
Law of Exponents c c c = c 5 c 4 = (c c c) (c c c c) = c 9 What did you do to the exponents? ADD THE EXPONENTS
Product of Powers Words: To multiply powers with the same base, add their exponents. Examples: 24 23 = 24+3 or 27 am an = am+n
a. c 3 c 5 Example 1 - Simplify c 3 c 5 c 3 + 5 = c 8 b. -3 x 2 4 x 5 (-3)(4) x 2 x 5 -12 x 7
Law of Exponents r 4 r 2 =r r = What 2 r did you do with the exponents? SUBTRACT THE EXPONENTS
quotient of Powers •
Example 2 - Simplify •
Powers of Monomials Lesson 4
Power of a Power Words: To find the power of a power, multiply the exponents. Examples: (52)3 = 52 x 3 = 56 (am)n = am n (64)5 = (64)(64)(64) 5 factors
Example 1 Simplify. a. (84)3 84 x 3 812 b. (k 7)5 k 7 x 5 k 35
Power of a Product Words: To find the power of a product, find the power of each factor and multiply. Examples: (6 x 2)3 = 63 (x 2)3 = 216 x 6 (6 x 2)3 = (6 x 2)(6 x 2) 3 factors
Example 2 Simplify. a. (4 p 3)4 44 p 3 x 4 256 p 12 b. (-2 m 7 n 6)5 (-2)5 m 7 5 n 6 5 -32 m 35 n 30
Negative Exponents Lesson 5
Zero and Negative Exponents •
• Example 1 - Simplify
Example 2 •
Powers of 10 Exponential Form Standard Form 103 102 1, 000 100 How many Zero’s? 3 2 101 100 10 1 1 0 10 -1 1 10 -2 2 10 -3 3
Example 3 •
Example 4 - Simplify •
Example 5 - Simplify •
Scientific Notation Lesson 6
Scientific Notation Table Expression Product 4. 7 x 103 = 4. 7 x 1000 4. 7 x 102 = 4. 7 x 100 4. 7 x 101 = 4. 7 x 10 -1 = 4. 7 x 0. 1 4. 7 x 10 -2 = 4. 7 x 0. 01 4. 7 x 10 -3 = 4 x 0. 001 4, 700 47 0. 0047
Scientific Notation Words: when a number is written as the product of a factor and an integer power of 10. The number must be between 1 and 10. Symbols: a x 10 n, where a is between 1 and 10 Example: 435, 000 = 4. 35 x 108
Two Rules for S. N. 1. If the number is greater than or equal to 1, the power of 10 is positive. 2. If the number is between 0 and 1, then power of ten is negative.
Example 1 Write each number in standard form. a. 5. 34 x 104 5. 34 x 10, 000 move the decimal point 4 times to the right = 53, 4000 b. 3. 27 x 10 -3 3. 27 x 0. 001 move the decimal point 3 times to the left 0. 00327
Example 2 Write each number in scientific notation. a. 3, 725, 000 3. 725 x 106 b. 0. 000316 3. 16 x 10 -4
Example 3 - comparing Refer to the table at the right. Dollars Spent by International Visitors in the U. S. Order the countries Country Dollars Spent according to the amount of Canada 1. 03 x 107 money visitors spent in the India 1. 83 x 106 US from greatest to least. Mexico United Kingdom STEP 1: 1. 06 x 107 1. 03 x 107 > 7. 15 x 106 1. 83 x 106 STEP 2: 1. 06 > 1. 03 7. 15 x 106 1. 06 x 107 7. 15 > 1. 83 CORRECT ORDER: United Kingdom, Canada, Mexico, India
Example 4 If you could walk to the moon at a rate of 2 meters per second, it would take you 1. 92 x 108 seconds to walk to the moon. Is it more appropriate to report this time as 1. 92 x 108 seconds, or 6. 09 years? Explain. The measure 6. 09 years is more appropriate. The number 1. 92 x 108 seconds is too large of a number to describe a walk to the moon.
Compute with Scientific Notation Lesson 7
Example 1 Evaluate (7. 2 x 103)(1. 6 x 104). Express in scientific notation. Rearrange the numbers (7. 2 x 1. 6)(103 x 104) (11. 52)(107) Move the decimal over to that the number is in scientific notation. 1. 152 x 108
Got it? a. (8. 4 x 102)(2. 5 x 106) 2. 1 x 109 b. (2. 63 x 104)(1. 2 x 10 -3) 3. 156 x 101
Example 2 •
Adding Numbers in Scientific Notation a. (6. 89 x 104) + (9. 24 x 105) Make each number have the same power of ten. (9. 24 x 105) = 92. 4 x 104 Add the numbers. 6. 28 + 92. 4 = 99. 29 x 104 Put this number in scientific notation. =9. 929 x 105
Adding Numbers in Scientific Notation b. 593, 000 + (7. 89 x 106) Each number must be in scientific notation. 593, 000 = 5. 93 x 105 Make each number have the same power of ten. (7. 89 x 106) = 78. 9 x 105 Add the numbers. 78. 9 + 5. 93 = 84. 83 x 105 Put this number in scientific notation. =8. 483 x 106
Subtracting Numbers in Scientific Notation (7. 83 x 108) – 11, 610, 000 Each number must be in scientific notation. 11, 610, 000 = 1. 161 x 107 Make each number have the same power of ten. (7. 83 x 108) = 78. 3 x 107 Subtract the numbers. 78. 3 + 1. 161 = 77. 139 x 107 Put this number in scientific notation. =7. 7139 x 108
Got it? a. (8. 41 x 103) + (9. 71 x 104) 1. 0551 x 105 b. (1. 263 x 109) - (1. 525 x 107) 1. 24775 x 109 c. (6. 3 x 105) + 2, 700, 000 3. 33 x 106
Roots Lesson 8
Vocabulary •
• Example 1
Got it? 1 • ± 0. 9 -7 No real solution
Example 2 •
Got it? 2 • a = ± 17 m = ± 0. 3
Cube Roots •
Example 3 •
Got it? 3 • 9 -4 10
Example 4 •
Got it? 4 An aquarium in the shape of a cube that will hold 25 gallons of water has a volume of 3. 375 cubic feet. Solve s 3 = 3. 375 to find the length of one side of the aquarium. s = 15
Estimating Roots Lesson 9
Estimating Square and cube Roots •
Example 1 •
Got it? 1 • 6 13 7
Example 2 •
Got it? 2 • 4 3 5
Example 3 •
Got it? 3 •
Example 4 •
Compare Real Numbers Lesson 10
Real Numbers
“Little Subset” Verse: Give me a number that’s rational Like any fraction that hurts Accepting positive or negative Are you ready…for two thirds? Or I’ll take the terminating decimal. 15, it will be If it’s repeating, it’s sensible So How about, . 33333 Chorus: Hey little subset, I’m a real number The big super-set, rational and irrational Hey smaller subset You call this place an integer? It’s bigger than the whole numbers and counting without the zeros A rational subset are integers They walk this number line Go both directions from zero They go left, they go right Now, take the positive integers And let’s give them a name zero, 1, 2, 3, 4, 5 etc… That’s the whole number game (Chorus) Bridge: Bummed irrational numbers Feel such heavy shame They’re real, but that’s just not the same They envy subsets that complain So they complain blah blah Verse 3: We can’t be written as fractions Else we’d be rational We don’t repeat and/or terminate Like Pi, 3. 14159265… (Chorus)
Example 1 •
Got it? 1 • irrational natural, whole, integers, and rational
Example 2 • < >
Example 3 •
Got it? 3 •
Example 4 •
vocabulary base cube root exponent irrational number monomial perfect cube perfect square power radical sign real number rational number repeating decimal scientific notation square root terminating decimal
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