# Converting to scientific notation for computations

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Chapter 2 / Exercise 43
Intermediate Algebra: Connecting Concepts through Applications
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Converting to scientific notation for computationsPerform these computations by first converting each number into scientific notation. Giveyour answer in scientific notation.a)(3,000,000)(0.0002)b)(20,000,000)3(0.0000003)Solutiona)(3,000,000)(0.0002)31062104Scientific notation6102Product rule for exponentsb)(20,000,000)3(0.0000003)(2107)3(3107)Scientific notation810213107Power of a product rule2410142.41011014242.41012.41015Product rule for exponentsNow do Exercises 43–50U5VApplicationsE X A M P L E 6Using scientific notationa)The mean distance from Mars to the sun is 141.6 106miles. Express this distance infeet. Use scientific notation rounded off with one digit to the right of the decimal point.b)If the national debt is \$1.8 1013and the population of the country is 3.5 108, thenwhat is the debt per person? Express the answer in standard notation to the nearestthousand dollars.Solutiona)There are 5280 feet in one mile. So we use a calculator to multiply 141.6 106by 5280:141.6 106miles 5218m0ifleeet7.5 1011feetb)Use a calculator to divide the debt by the number of people:3.5\$1.81081p0e1o3ple\$51,000 per personNow do Exercises 59–66b)841100524811005212105(2)Quotient rule for exponents(0.5)107120.55101107Write 0.5 in scientific notation.5106Product rule for exponentsc)(5107)353(107)3Power of a product rule1251021Power of a power rule1.2510210211251.251021.251019Product rule for exponentsNow do Exercises 31–42UCalculator Close-Up VWith a calculator’s built-in scientificnotation, some parentheses can beomitted as shown. Writing out thepowers of 10 can lead to errors.Try these computations with yourcalculator.
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Chapter 2 / Exercise 43
Intermediate Algebra: Connecting Concepts through Applications
Clark Expert Verified
ExercisesUStudy Tips VIt is a good idea to review on a regular basis. Go back to a section that you have already studied and work some exercises.Every chapter of this text contains a Mid-Chapter Quiz. You can use these to review the first half of any chapter.4.3U1VConverting Scientific to Standard NotationWrite each number in standard notation. See Example 1. See theStrategy for Converting to Standard Notation box on page 273.1.9.861092.4.0071043.1.371034.9.31055.11066.31017.61058.81069.56 10410.286 10511.43.2 10412.589.6 10313.0.0067 10314.0.34 103U2VConverting Standard to Scientific NotationWrite each number in scientific notation. See Example 2. See theStrategy for Converting to Scientific Notation box on page 274.15.900016.5,298,00017.0.0007818.0.00021419.0.000008520.0.01521.644,000,00022.5,670,000,00023.52510924.0.0034108U3VCombining Numbers and WordsWrite each number in scientific notation and standard notation.25.23 million26.344 million27.15 billion28.3478 billion29.13.6 trillion30.0.75 trillionWarm-Ups Fill in the blank.1.The number 1.2 1012is written in notation.2.To convert to standard notation, multiply bythe appropriate power of 10.3.To convert to scientific notation, move thedecimal point and use the appropriate power of 10.
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