Chpter Properties of Epoets d Scietific Nottio Epoet - A umer or symol, s i ( + y), plced to the right of d ove other umer, vrile, or epressio (clled the se), deotig the power to which the se is to e rised. Also clled power. The epoet (or power) tells how my times the se is to e multiplied y itself. Emple 1: ( + y) = ( + y)(+y)(+y) Emple : (-) 4 = (-)(-)(-)(-) = 81 Sectio.1 Product Rule If m d re itegers, the m m Emple: ( )( 4 ) = 6 Power Rules If m d re itegers, the ( ) m m Emple: ( ) = 10 If m,, d p re itegers, the ( y) y, Emple: (y) 4 = 4 y 4 d ( y ) y m p m p p Emple: ( y ) 4 = 1 y 8 If is iteger d 0, the Emple : 9 Sectio. Zero d Negtive Epoets If is rel umer d 0, the 0 1 Emple: 0 = 1 If is positive iteger (- is egtive), d 0, the 1 d 1 (A egtive epoet is just other wy to write the reciprocl of umer) Emples : If is iteger, d 0, the Emple : If m d re itegers 0 d 0, the m Emple : y 7 y m 7
Chpter Properties of Epoets d Scietific Nottio Sectio. Quotiet Rule If m d re itegers d 0, the m m Emple : Sectio.4 SCIENTIFIC NOTATION Scietific Nottio is wy to descrie very lrge or very smll umers. There re officil mes for some of the lrge umers, ut ot my people kow them. # s of 0 s Nme Smples thousd 1,000 6 millio 1,000,000 9 illio 1,000,000,000 1 trillio 1,000,000,000,000 1 qudrillio 1,000,000,000,000,000 18 quitillio 1,000,000,000,000,000,000 1 setillio 1,000,000,000,000,000,000,000 4 septillio 1,000,000,000,000,000,000,000,000 7 octillio 1,000,000,000,000,000,000,000,000,000 0 oillio 1,000,000,000,000,000,000,000,000,000,000 decillio 1,000,000,000,000,000,000,000,000,000,000,000 6 udecillio 1,000,000,000,000,000,000,000,000,000,000,000,000 For emple there re estimted 1,000,000,000,000,000,000,000 strs i the uiverse. Tht s setillio strs, or illio trillio strs! A esier wy to write tht umer is to use scietific ottio. Strt from the deciml poit (or the ed of the umer if there is o deciml poit), d cout how my spces you go to the left util you get to just to the right of the first digit. 1,000,000,000,000,000,000,000 = 1.0 X 10 1 = 10 1
Chpter Properties of Epoets d Scietific Nottio Scietific Nottio (epoetil ottio) refers to writig deciml umers s umer multiplied y power of 10. Now this is doe i certi wy. Wht this oils dow to is movig deciml poit, keepig trck of how my plces you moved it, d icresig or decresig the power of 10 y tht umer of deciml poit moves. Formlly ow, epoetil umer hs two prts, mtiss d epoet. The mtiss is umer whose mgitude is greter th or equl to 1 ut less th 10. The epoet is power of 10. Here's emple:.4 10 the mtiss is.4 the epoet is Here's other emple: -.104 10 - the mtiss is -.10 d the epoet is - Ok, so wht re these umers?.4 10 = 40 d -.104 10 - = -0.0104 Here's the del. The epoet is the umer of deciml plces to move left or right to remove the power of 10. How's tht? Ok, let's cosider few emples. Emple: Tke the umer 1.4, we wt to write this umer i scietific ottio. First of ll this umer is greter th 9.999... so we eed to rewrite it usig powers of te. We eed to move the deciml poit. Let's move it right y 1. We get 14., d we're gettig umer eve lrger th 9.999... So let's move it left y 1. We get 1.4, we're gettig closer to 9.999... ut we o loger hve the sme umer. 1.4 1.4, ut if we multiply 1.4 y 10 we'll hve the sme umer. We hve 1.4 10 1. 1.4 = 1.4 10 (we usully do't show the 1 i the epoet) Well, 1.4 is still greter th 9.999... so, let's move the deciml left oe more time. We get: 1.4 for the mtiss d this umer is i the correct rge ut we ow eed to multiply y 100 = 10 to keep the sme umer. So we hve 1.4 = 1.4 10 (otice, we moved the deciml left twice d icresed the epoet of te y ) Emple: cosider 0.000716 The mtiss must e greter th or equl to 1 d less th 10, d this umer is much to smll. If we move the deciml right y 1 we get 0.00716 ut we eed to multiply y 10-1 to keep the sme umer. So if we move the deciml right y 4 we get 7.16 which is
Chpter Properties of Epoets d Scietific Nottio i rge for the mtiss ut we eed to multiply y 10-4 to keep the sme umer. So wht we hve is 0.000716 = 7.16 10-4 (we moved the deciml right 4 times d decresed the epoet of te y 4) The poit of scietific ottio is the ility to write very lrge or very smll umers i compct form. Emples of very lrge umers re: Avogdro's Numer: 6.07 10 (umer of toms of sustce to give the umer of grms equl to the tomic mss of the sustce) speed of light:.0 10 8 meters per secod googol = 110 100 dimeter of tom =. 10-10 meters Opertios with umers i epoetil ottio. A review of epoets would e very helpful here efore proceedig with the emples. Multiplictio/Divisio This is esier, so we'll do this first. Procedure: Multiply/divide the mtisss, the the powers of 10, the write the result i proper form. Emples: 1) 8.10 4 X.010 = (8..0) X ( 10 4 10 ) = 16.6 10 9 ow, rewritig, we get 1.6610 10 1. 10 ) 4.0 10 10 1 1 1. 10 1 6 0.10 0.10 4.0 Tht mtiss is ot greter th or equl 1 so we multiply the mtiss y 10 d divide d sutrct 1 from the epoet. We the get.0 10-7 Additio/Sutrctio The epoets of the ddeds or sutrheds must e the sme. Procedure: Adjust the epoets util they re the sme; s you do this you will e djustig the mtisss s well. Comie mtisss d rewrite the result i proper
Chpter Properties of Epoets d Scietific Nottio epoetil form. By doig this you re cretig like terms. Jus preted tht the 10 s re s. Emple:.110 + 8.4110 we'll do this two wys. First, we'll chge the first umer to epoet of.110 + 8.4110 = 40.10 = 4.010 ow let's write the secod umer to hve epoet of.110 + 0.84110 = 4.010 either method is fie.