Name: MATH 65 LAB INTEGER EXPONENTS and SCIENTIFIC NOTATION. Instructor: T. Henson
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1 MATH 6 LAB INTEGER EXPONENTS ad SCIENTIFIC NOTATION Name: Istructor: T. Heso Purpose: Epoets are used i may formulas, especially i the scieces where epoets are used to write very small umbers ad very large umbers i scietific otatio. I this lab you will use the properties of epoets to simplify epoetial epressios ad you will use scietific otatio to perform computatios with very large ad very small umbers. Learig Goals: Symbolic ad umerical represetatio; quatitative reasoig Apply rules for simplifyig epoetial epressios to simplify epoetial epressios. Write umerical quatities i scietific otatio. Use scietific otatio i computatios. Materials Needed: scietific calculator A. RULES FOR NEGATIVE EXPONENTS. What is the meaig of? We ca use patters to help us aswer this questio.. Complete the table below. What do you otice? = (assume = = = What do you otice? ) Now, cotiue the patter = = = Now, cotiue the patter = = =. Does a egative epoet make the value of the epressio egative?. What is the effect of havig a egative epoet? = Math 6 Elemetary Algebra
2 Math 6 Lab Iteger Epoets ad Scietific Notatio Page of Aother way to uderstad the egative epoet rule makes use of the rule for m m simplifyig epoets i a fractio. You have leared a rule that states: =. Let s use this rule to simplify the epoetial epressio : = = Now, the aswer has a egative epoet i it. We ca uderstad what this egative epoet meas if we thik of simplifyig the fractio i the followig way = = = = The two differet results must be equal, sice we started with the same epressio. Therefore =. B. SIMPLIFYING EXPONENTIAL EXPRESSIONS. Complete each rule for epoets. m m = = m ( ) y = = ( ) = y = = = Use the rules for simplifyig epoetial epressios to rewrite each epoetial epressio i simplest form. Show all steps of your work/thikig. NO CREDIT for aswers without supportig work ( )( ) ab ab. m ( y ) ( y ) 4. 7 ( ) y Math 6 Elemetary Algebra
3 Math 6 Lab Iteger Epoets ad Scietific Notatio Page of. y y ( y ) m 4m ( 4a b ) ( a b ) 8. 4 m 7 m 9. ( 4 yz )( 6y 9 z ) 9y z Math 6 Elemetary Algebra
4 Math 6 Lab Iteger Epoets ad Scietific Notatio Page 4 of C. SCIENTIFIC NOTATION. Use calculatios i scietific otatio to solve each problem. Use a calculator to assist you with calculatios.. A light-year is a uit of legth used by astroomers to measure iterstellar distace (the distace betwee stars). A light-year is defied as the distace that light will travel i a year. If the speed of light is 86, miles per secod (, km per secod), the calculate the distace that light will travel i oe year. Epress your aswer i miles per year usig both scietific otatio ad stadard otatio. Fill i the blaks to calculate oe light-year i miles per year. You ca cacel like uits. mi sec mi hour day sec mi hour day year Scietific Notatio: Stadard Notatio: This is how may miles light travels i oe year!. Astrophysicists estimate that the radius of the Milky Way galay is 469,,,,, km. a. Write this umber i scietific otatio. b. Usig the fact that km =.67 mi, epress the radius of the Milky Way galay i miles i both scietific otatio ad stadard otatio. Idicate how you calculated the aswer (use scietific otatio to do the calculatios). Scietific Notatio: Stadard Notatio: Math 6 Elemetary Algebra
5 Math 6 Lab Iteger Epoets ad Scietific Notatio Page of c. Epress the radius of the Milky Way galay i light-years. Give your aswer i both stadard otatio ad scietific otatio. Idicate how you calculated the aswer (use scietific otatio to do the calculatios). Scietific Notatio: Stadard Notatio:. The weight of a sigle E. coli bacterium is.66 g. a. Write this umber i scietific otatio. b. What would millio E. coli bacteria weigh? Give your aswer i both stadard otatio ad scietific otatio. Idicate how you calculated the aswer (use scietific otatio to do the calculatios). Scietific Notatio: Stadard Notatio: c. How may bacteria would it take to make g i weight? Give your aswer i both stadard otatio ad scietific otatio. Idicate how you calculated the aswer (use scietific otatio to do the calculatios). Scietific Notatio: Stadard Notatio: Math 6 Elemetary Algebra
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