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.