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## Rational Numbers

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**Rational Numbers**Chapter 1, Lesson 1**Vocabulary**Complete this graphic organizer. Rational Number Define in your own words. Fraction Percent Mixed Number Decimal**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. =**Example 1**Write each fraction as a mixed number as a decimal. a. 5 8 = 0.625 b. -1 = -5 ÷ 3 = -1.6**Got it? 1**Write each fraction as a decimal. 1. 2. - 3. 4 4. 3 -0.2 0.75 4.52 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**Write 0.45 as a fraction. 0.45 = =**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 =**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**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. 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**Write and Evaluate Powers**4 factors 2 2 2 2 = 24 n factors**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**Example 2**Evaluate. ()4 = = Got it? ()3 =**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**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**Multiply and Divide Monomials**Lesson 3**Monomials**Monomial: a number, variable, or a product of a number and variable Examples: 32 74 a4b8 3x2y g**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**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**Example 1 - Simplify**• c3 c5 c3 c5 c3 + 5 = c8 • -3x2 4x5 -3x2 4x5 (-3)(4) x2 x5 -12x7**Law of Exponents**r 4 = r r r r r2 = r r = r2 What did you do with the exponents? SUBTRACT THE EXPONENTS**quotient of Powers**Words: To divide powers with the same base, subtract their exponents. Examples: = 37 – 3 = 34 = am – n**Example 2 - Simplify**= 46 = 4,096 = 6x2**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)(64)(64) 5 factors**Example 1**Simplify. • (84)3 84 x 3 812 • (k7)5 k7 x 5 k35**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**Example 2**Simplify. • (4p3)4 44 p3x4 256p12 • (-2m7n6)5 (-2)5 m75 n65 -32m35n30**Negative Exponents**Lesson 5**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 =**Example 1 - Simplify**• 6-2 = • a-5 = • 80 = 1**Example 2**Write each fraction using a negative exponent. = 5-2 = = 7-2**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**Example 4 - Simplify**53 x 5-5 = 53+(-5) = 5-2 =**Example 5 - Simplify**=b(2 – 6) =b-4 =**Scientific Notation**Lesson 6**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**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.**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**Example 2**Write each number in scientific notation. • 3,725,000 3.725 x 106 • 0.000316 3.16 x 10-4**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**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