Exponents and Polynomials - XYZ Custom Plus

596Chapter 9 Exponents and PolynomialsNext, we turn our attention to writing small numbers in scientific notation. Todo so, we use the negative exponents developed in the previous section. Forexample, the number 0.00075, when written in scientific notation, is equivalentto 7.5 × 10 −4 . Here’s why:7.5 × 10 −4 = 7.5 × ​_110 4​= 7.5 × ​ 1_10,000 ​= ​ _ 7.5​= 0.0007510,000The table below lists some other numbers both in scientific notation and instandard form.3. Fill in the missing numbers inthe table below:StandardFormScientificnotationa. 24,500 =b. = 5.6 × 10 5c. 0.000789 =d. = 4.8 × 10 −3Example 3Each pair of numbers in the table below is equal.Standard FormScientific Notation376,000 = 3.76 × 10 549,500 = 4.95 × 10 43,200 = 3.2 × 10 3591 = 5.91 × 10 246 = 4.6 × 10 18 = 8 × 10 00.47 = 4.7 × 10 −10.093 = 9.3 × 10 −20.00688 = 6.88 × 10 −30.0002 = 2 × 10 −40.000098 = 9.8 × 10 −5As we read across the table, for each pair of numbers, notice how the decimalpoint in the number on the right is placed so that the number containing the decimalpoint is always a number between 1 and 10. Correspondingly, the exponenton 10 keeps track of how many places the decimal point was moved in convertingfrom standard form to scientific notation. In general, when the exponent is positive,we are working with a large number. On the other hand, when the exponentis negative, we are working with a small number. (By small number, we mean anumber that is less than 1, but larger than 0.)We end this section with a diagram that shows two numbers, one large and onesmall, that are converted to scientific notation.376,000 = 3.76 × 10 5Moved 5 placesDecimal pointoriginally hereKeeps track of the5 places we movedthe decimal point0.00688 = 6.88 × 10 −3Moved 3 placesKeeps track of the3 places we movedthe decimal pointAnswer3. a. 2.45 × 10 4b. 560,000c. 7.89 × 10 −4d. 0.0048Getting Ready for ClassAfter reading through the preceding section, respond in your ownwords and in complete sentences.1. What is scientific notation?2. What types of numbers are frequently written with scientific notation?3. In writing the distance, in miles, to the sun, would we use a positivepower of ten or a negative power of ten?4. In writing the weight, in kilograms, of a paper clip, would we use a positivepower of ten or a negative power of ten?