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Introduction to Scientific Notation

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Introduction to Scientific Notation "#$%&'()$*&#!$&!+)*,#$*-*)!.&$/$*&#!! ! ! 0,-*#*$*&#!&-!+)*,#$*-*)!.&$/$*&#1!! In scientific notation all numbers are written in the form of a x 10bwhere the exponent b is an integer, and the coefficient a is any real number (however, see normalized notation below), called the significand or mantissa. :%'!+)G*%!%H75*#!2$%!5*!A#)//*%!)%!/0*!I9#7!9I!!JED"!)%!7$%'!A$',K!I9#!*L$7;3*4!FMD!2$%! 5*!A#)//*%!$,!F8MJEDB!9#!FMJEDE!9#!FMDJEDD8!! ! N%!#$%&!'()*+!,2)*%/)I)2!%9/$/)9%4!/0*!*L;9%*%/!"!),!209,*%!,9!/0$/!/0*!$5,93H/*!G$3H*!9I!!! #*7$)%,!$/!3*$,/!9%*!5H/!3*,,!/0$%!/*%!OE!P!Q!Q!R!EDS8!<9339A)%+!/0*,*!#H3*,4!FMD!A9H3&! !"#!$%!5*!A#)//*%!$,!F8MJEDB8!! ! ! E8!<)33!9H/!/0*!7),,)%+!*%/#)*,!)%!/0*!/$53*!5*39AT! ! Standard decimal Normalized scientific notation notation Written English 2!100 300 Three hundred. 4,321.768 "5.3!104 6,720,000,000 0.2 Two tenths. 7.51!10"9 Seven hundred and fifty one - one billionths -0.0006071 ! ! ! ! ! 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"#$%&'!()*+*#,!!!-!.$#)%!.$/0!1)#23*4!5#$%&'67,#)89#+! ! :&$;/*&!<#97!=<=>!?%+)%**#)%+!@$/0A$',!@#9+#$7! !.$#20!BC8!BDEF! ! $8 ! fH*,,!'9H#!$%,A*#!OA)/0!H%)/,ST!! ! 58 (0$/!$%,A*#!),!+9)%+!/9!5*!/99!5)+a!! ! 28 (0$/!$%,A*#!),!+9)%+!/9!5*!/99!,7$33a! ! &8 !1$32H3$/*!/0*!$%,A*#T! ! ! 4. How many drops of waters are there in all of the Great Lakes? $8 fH*,,!'9H#!$%,A*#!OA)/0!H%)/,ST!! ! ! 58 !(0$/!$%,A*#!),!+9)%+!/9!5*!/99!5)+a!! ! ! 28 !(0$/!$%,A*#!),!+9)%+!/9!5*!/99!,7$33a! ! ! &8 !!1$32H3$/*!/0*!$%,A*#T!! UK.M+!\M4+["K.+1!! 5. If you make $100,000 annually, how many years would it take for you to make $182M? How about to make $2.7B? $100B? ! "#$%&'!()*+*#,!!!-!.$#)%!.$/0!1)#23*4!5#$%&'67,#)89#+! ! :&$;/*&!<#97!=<=>!?%+)%**#)%+!@$/0A$',!@#9+#$7! !.$#20!BC8!BDEF! 6. If you are six feet tall, how many lengths of you would be equal to the height of a stack of $182M in dollar bills? (A stack of 50 bills is 0.215 inches.) 7. How many miles is a $2.7 billion stack of one-dollar bills if you stack them side-by-side? 8. If you can run 10 minutes per mile, how long would it take for you to run the miles from #7 in days? ! ! ! ! "#$%&'!()*+*#,!!!-!.$#)%!.$/0!1)#23*4!5#$%&'67,#)89#+! ! :&$;/*&!<#97!=<=>!?%+)%**#)%+!@$/0A$',!@#9+#$7! !.$#20!BC8!BDEF! The DBD Oil Spill Ten days ago, a big underwater oil well from DBD Petroleum Company ruptured near the coast of Paradise Island. DBD sent a robot to take pictures of the damaged pipes, and using these images they reported to the public an estimate of 8000 barrels per day being discharged into the ocean. The government of Paradise Island has contracted your team to evaluate the DBD estimate of oil discharge. It is important to have a reasonable estimate in order to assess the magnitude of the problem and prepare the national response to the spill. Your Team Task: Prepare a report for the Paradise Island officials. It should contain: 1. An estimate the oil discharge of the DBD oil well into the ocean, in units of barrels of oil per day. 2. An explanation of the calculations and information that leads to your estimate. 3. An evaluation of the DBD estimate. Is it reasonably close to your estimate? Is it too low? Too high? Note. The Exxon Valdez disaster of 1989 discharged 250,000 barrels of oil into the ocean (10.5 million gallons). To complete this task your team will be provided the following (see page 2): - The DBD estimate of the spill - Satellite pictures of the oil spill on Day 2 and Day 7 after the incident. - Information about the appearance of the oil. - Information about the science of past oil spills (depth estimates, other volume estimation information). Note: This activity is based on the article “Deepwater disaster: how the oil spill estimates got it wrong”, by Ian MacDonald, in the December 2010 issue of Significance, journal of the Royal Statistical Society. Brandy Wiegers - Marin Math Circle, [email protected] Adapted From SFSU Engineering Pathways Program March 2013 Satellite Pictures of the Oil Spill on Day 2 and Day 7 Your team does not have access to the DBD data on the accident but you have satellite pictures of the oil spill taken on Day 2 and Day 7 after the incident: In addition to sharing the satellite pictures the Paradise Island officials have told you that the appearance of the oil spill on the surface of the water gives it a bright color.
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