BOBO (-,dHHHHHH (,H (, (*xZ-Francis J. DeHoratiusjFLOM!`Fx(HHR[ (hh t2 HK'dE6Ad  (-l /b, (3 (3H/H/ (b (+ `  T[]yDSETQQ3QN (,t (,| (,x (4( (E@}5 )g )gx )g2   ) * 2 3 > ?     ( ) 6 7     ' ( 4 5   ? @ L Y e f        2 3 K L k         > ? O P c d             Q R a s       |u !( 01 <=  &' 35  %& 13 u> J K W X Y cd             u1 < = H I   u     L N Pub d               ! # 0 2  (,p (4,Scientific Notation Examples 1) 264 000 M x 10n 2.64 x 105 M must be between 1 and 10; the exponent of 10 indicates the number of places you moved the decimal point to convert 264 000 to 2.64 x 10; the exponent is positive because you moved the decimal point to the left. 2) 0.0716 M x 10n 7.16 x 10 -2 M must be between 1 and 10; the exponent of 10 indicates the number of places you moved the decimal point to convert 0.0716 to 7.16 x 10; the exponent is negative because you moved the decimal point to the right. 3) 0.000 000 132 M x 10n 1.32 x 10-7 M must be between 1 and 10; the exponent of 10 indicates the number of places you moved the decimal point to convert 0.000 000 132 to 1.32 x 10; the exponent is negative because you moved the decimal point to the right. Adding/Subtracting Using Scientific Notation 2.610 x 103 6.2000 x 104 + 5.2 x 101 all numbers must have the same exponent of 10 and so the above becomes 2.610 x 103 62.000 x 103 + 0.052 x 103 64.662 x 103 which must be changed to 6.4662 x 104 Multiplication Using Scientific Notation (3.2 x 103) (1.5 x 102) Multiple 3.2 by 1.5 to get 4.8 Algebraically add the exponents of 10 to get 3 +2 = 5 Ans: 4.8 x 105 Dividing Using Scientific Notation (8.4 x 10-7) / (2.1 x 10-4) Divide 8.4 by 2.1 and get 4.0 Subtract the exponents (-7 -(-4)) gives us -3 Ans: 4.0 x 10-3 Practice Problems: Convert the following into scientific notation: a) 1 930 b) 262 000 c) 71 400 d) 93 100 000 e) 704 f) 0.0713 g) 0.000 067 2 h) 0.195 i) 0.000 000 008 33 j) 0.006 21 Evaluate the following and express the results in scientific notation: a) 8 200 x 510 b) 910 x 0.000 30 c) 720 / 36 000 d) 3 100 / 0.012 e) (2.6 x 103) + (3.4 x 104) f) (2.9 x 10-4) - (6.4 x 10-5) g) ((2.6) x (2.6 x 102)) / 0.000 026 h) (2.73 x 104) / (9.10 x 10-2) i) (3.2 x 10-3) x (1.5 x 10-2)ZNDSET2Hr (4$ 6*DSET2H+ (4  6*DSUM.Francis J. DeHoratiusHDNISTYL 2JSTYL (4 (3 (4 (4 (3 (3 (3 (3 (3                       HASH $. . . . ..O OOy.y.L:Qhjazo}Bod CHAR (4   "      u upHASH      $ $ $ uuR CELL (4"HASH  GRPH (3(HASH  l RULR (3 (HASH @ KSEN (3z"HASH8LKUP  0$NAMEDefault Default SS Default TBHeaderBodyFooterFootnoteFootnote IndexDFNTMPalatinoGenevaMCROMCROoBlNMARKMRKS MOBJWMBTSNAP1,,  HH )fH )f@i0{;w[{w{|w{|w{\nuwj4w:r{|rw[{{w:nuw{{[{\{[{{:r{|g/rjU{\nrsnvw:r{|rrrr{\r{|rnn{{j4r{[nUj3{;rnuwww[w:nUrnnn{errrri0{{|{|rrw:{;r{wnrrnw{;w:r{[rnrrrrw:ww[wrr{wnrnvwnu{[rw{[w:w; r o{swNskZZR^VV o{kZg9NsF1JRo{RB=V o{s{Vo{wkZg9sskZswo{{wg9ss kZkZZ^w^o{g9o{so{kZsw{o{kZwsw{swcc kZ^o{kZwkZo{kZg9g9 wkZwckZ^wo{co{wJg9o{Zso{w{skZg9wsc{skZswswswwkZswswg9{o{^kZkZg9wwswso{{sswwswkZs^g9kZkZws{o{^{swkZsw{Jg9cV{g9cR^Z^{ccRcV^ccZ^g9JRckZcVJRkZ^g9g9^kZg9g9RZNsg9o{Z^ccZVcg9g9kZg9ccg9kZkZcZg9Rc^VcNs^o{wo{wc{{{w{kZ{{wss{o{w{{ww{w!w{w{wg9o{kZw{o{ww{wws{w{{o{w{wCo{kZg9csg9kZkZcRg9g9Rcg9g9Vg9kZcNskZZkZRc^g9kZg9RkZg9Zc^Z^o{kZZZkZVZkZcg9g9VckZckZkZNsg9kZo{kZkZg9swww:swwsws{{g9{wsw{wsg9s{ws{s{{s{w{sw{s{swwsw{^{w{s{{{sGg9swo{kZg9{skZsskZsso{{{{so{g9^g9c;g9^scg9Ro{ZkZso{cg9o{o{Zccsg9o{o{kZcg9kZV^g9g9cckZckZVckZcZo{kZg9kZcckZcZkZV{ skZswwo{swo{s3{swso{wsw{kZwo{o{{{kZwkZwo{wo{o{s{^{kZswo{swskZ{g9swso{so{skZ?sw{{w{wswkZw{kZg9o{cg9sg9{^o{kZsso{g9kZkZZscg9^^kZw^o{g9g9o{ZkZg9^g9o{g9Z{g9o{kZo{cg9kZskZcZg9{=wso{ssg9g9kZg9kZwg9o{skZwo{skZkZw{kZo{kZo{o{g9s{g9o{wo{kZg9o{kZg9^wkZo{o{kZ{o{o{s{kZskZwskZo{o{sws wwwws{ާ wkZkZg9NsRNs^JRVs wg9o{kZRo{NsV{RZc {ޞg9o{^{wg9^g9kZ g9g9V^s{^^sw ss#s^kZwwkZkZsw{kZ# o{o{ccsckZo{o{ss{s{{s{ަIs{s{wwsw{wkZwwo{ww{sJo{kZVg9cg9sg9^{g9g9Vcc^ccg9ccVkZo{sg9co{kZkZskZcccg9^VkZo{ckZg9kZg9^g9o{cwg9cskZkZskZkZo{ZskZg9^VkZw/o{o{kZo{o{g9kZg9o{o{so{o{o{so{o{kZswkZo{skZccskZo{o{kZkZo{sg9skZss^o{kZo{o{so{sskZkZswso{kZkZg9kZkZg9o{kZo{w7{{{ww{w{{ o{ckZs{skZwsckZco{)kZcwskZo{kZskZsco{g9g9wwco{kZg9o{wsZg9g9o{kZsg9kZwg9kZg9sso{g9o{o{g9kZsg9CsckZZskZkZg9g9VkZcc^g9c^{kZo{^JRg9^g9VckZg9kZg9VkZco{g9Zc^kZg9cVg9ZVkZckZkZR^kZg9kZg9^co{o{sg9g95{{s{sw{{o{{o{o{o{so{s0ckZskZco{^wcg9kZsswo{Zswg9scwg9ZwwsskZo{wwkZwwkZg9{wkZo{wso{g9kZsw{Bo{o{^Zg9ckZVcg9ckZg9kZkZckZ^Vg9wkZw{g9^w^wkZo{^wcg9JRco{Zc^g9cg9cNsccV{cNsg9RZV^Nscc^ZkZ{o{g9skZw{www{{ww{w{w({ckZc{^ww{w{wkZww{wo{{kZ{{w^w{s{{co{{>kZg9^ZwZRg9cRg9ZkZg9co{g9g9ZckZo{Nsg9g9o{g9JRkZo{cckZg9g9Nsg9cVcZcg9g9Vo{g9g9o{kZg9^o{g9g9cg9g9V|w{sws{wkZ{{w{ww{ww{ww{wws{wwswsZwws{ ws{wwwVcw/{o{ww^c Zg9^g9^wkZsZ^s/g9o{^VV5F1Ro{Z-kVV^o{kZJRss1sskZ{ckZ^g9o{Zg9g9kZ^{o{^kZZsssw{kZww o{kZVg9w^o{cg9kZkZckZw{kZg9{sw{w{{wc! o{g9{kZwo{kZo{g9wo{ csg9g9swkZckZs{ިTNAM1AB05155308EC393C71AC1B5AC7F4EETBL`DSUMHDNIHSTYLRMCRO&oBlN&MARK&WMBT&SNAP&TNAM9ETBL9:x