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Rational Numbers

Rational Numbers

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Rational Numbers

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  1. Rational Numbers Chapter 1, Lesson 1

  2. Vocabulary Complete this graphic organizer. Rational Number Define in your own words. Fraction Percent Mixed Number Decimal

  3. 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. =

  4. Rational Numbers

  5. Repeating vs. Terminating Decimals

  6. Example 1 Write each fraction as a mixed number as a decimal. a. 5 8 = 0.625 b. -1 = -5 ÷ 3 = -1.6

  7. Got it? 1 Write each fraction as a decimal. 1. 2. - 3. 4 4. 3 -0.2 0.75 4.52 3.09

  8. 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

  9. 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

  10. Example 3 Write 0.45 as a fraction. 0.45 = =

  11. Example 4 Write 0.5 as a fraction. N = 0.55555… Multiply each side by 10. 10N = 10(0.555555….) 10N = 5.5555….. - N = 0.55555…. Subtract N = 0.55555… to eliminate the repeating part. 9N = 5 N =

  12. Example 5 Write 2.18 as a mixed number. N = 2.18181818… Multiply each side by 100. 100N = 100(2.1818181818….) 100N = 218.181818….. - N = 2.181818…. Subtract N = 0.181818… to eliminate the repeating part. 99N = 216 N = = 2

  13. Homework Independent Practice: 1 – 10, 14 – 15, 17, 19

  14. Powers and Exponents Lesson 2

  15. 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. 2. How many 2’s are multiplied to find his savings in Week 4? Week 5? 3. How much will he save in Week 8? $0.16 $0.08 $0.04 $0.32 $0.63 $0.07 $0.15 $0.31 5 4 $2.56

  16. Write and Evaluate Powers 4 factors 2  2  2  2 = 24 n factors

  17. Example 1 Write each expression using exponents. • (-2)  (-2)  (-2)  3  3  3  3 There are three (-2)’s and four 3’s. (-2)3  34 • a  a  b  b  a There are three a’s and two b’s. a3  b2

  18. Example 2 Evaluate. ()4    = = Got it? ()3 =

  19. 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  2  2  7 32  7 224 square inches

  20. Example 4 Evaluate each expression if a = 3 and b = 5. • a2 + b4 32 + 54 9 + 625 = 634 • (a – b)2 (3 – 5)2 (-2)2 (-2)(-2) = 4

  21. Multiply and Divide Monomials Lesson 3

  22. Monomials Monomial: a number, variable, or a product of a number and variable Examples: 32 74 a4b8 3x2y g

  23. Law of Exponents c  c  c  c  c = c5 c5  c4 = (c  c  c  c  c)  (c  c  c  c) = c9 What did you do to the exponents? ADD THE EXPONENTS

  24. 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

  25. Example 1 - Simplify • c3 c5 c3 c5 c3 + 5 = c8 • -3x2  4x5 -3x2  4x5 (-3)(4)  x2  x5 -12x7

  26. Law of Exponents r 4 = r  r  r  r r2 = r  r = r2 What did you do with the exponents? SUBTRACT THE EXPONENTS

  27. quotient of Powers Words: To divide powers with the same base, subtract their exponents. Examples: = 37 – 3 = 34 = am – n

  28. Example 2 - Simplify = 46 = 4,096 = 6x2

  29. Powers of Monomials Lesson 4

  30. 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)(64)(64) 5 factors

  31. Example 1 Simplify. • (84)3 84 x 3 812 • (k7)5 k7 x 5 k35

  32. Power of a Product Words: To find the power of a product, find the power of each factor and multiply. Examples: (6x2)3 = 63  (x2)3= 216x6 (6x2)3 = (6x2)(6x2)(6x2) 3 factors

  33. Example 2 Simplify. • (4p3)4 44 p3x4 256p12 • (-2m7n6)5 (-2)5 m75  n65 -32m35n30

  34. Negative Exponents Lesson 5

  35. Zero and Negative Exponents Words: Any number to the zero power is 1. Examples: 40 = 1 b0 = 1 Words: Any number to the negative power is the multiplicative inverse of its nth power. Examples: 7-3 = = k-n =

  36. Example 1 - Simplify • 6-2 = • a-5 = • 80 = 1

  37. Example 2 Write each fraction using a negative exponent. = 5-2 = = 7-2

  38. Powers of 10

  39. Example 3 One human hair is about 0.0001 inch in diameter. Write this decimal as a power of 10. 0.0001 has 4 zeros = 10-4

  40. Example 4 - Simplify 53 x 5-5 = 53+(-5) = 5-2 =

  41. Example 5 - Simplify =b(2 – 6) =b-4 =

  42. Scientific Notation Lesson 6

  43. Scientific Notation Table

  44. 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 10n, where a is between 1 and 10 Example: 435,000,000 = 4.35 x 108

  45. Two Rules for S.N. • If the number is greater than or equal to 1, the power of 10 is positive. • If the number is between 0 and 1, then power of ten is negative.

  46. Example 1 Write each number in standard form. • 5.34 x 104 5.34 x 10,000 move the decimal point 4 times to the right = 53,4000 • 3.27 x 10-3 3.27 x 0.001 move the decimal point 3 times to the left 0.00327

  47. Example 2 Write each number in scientific notation. • 3,725,000 3.725 x 106 • 0.000316 3.16 x 10-4

  48. Example 3 - comparing Refer to the table at the right. Order the countries according to the amount of money visitors spent in the US from greatest to least. STEP 1: 1.06 x 107 7.15 x 106 1.03 x 107 1.83 x 106 STEP 2: 1.06 > 1.03 7.15 > 1.83 > CORRECT ORDER: United Kingdom, Canada, Mexico, India

  49. 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.

  50. Compute with Scientific Notation Lesson 7