Scientific notation is a way of expressing really big numbers or really small numbers.

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2 Scientific Nottion (Stndrd form) Scientific nottion is wy of expressing relly big numbers or relly smll numbers. It is most often used in scientific clcultions where the nlysis must be very precise. Scientific nottion consists of two prts: number between 1 nd 10 power of 10 N 10 To write numbers in scientific nottion, use the following rules: For lrge numbers:. Move the deciml point to the left until is plced just fter the first digit in the number. This is the coefficient. b. Stte power of ten tht is equl to the number of plces the deciml point moved. x EXMPLE: = 3.5 x 10 4 For smll numbers: = x Move the deciml point to the right until it is plced just fter the first digit in the number. b. Stte negtive power of ten tht is equl to the number of plces the deciml point moved. EXMPLE: = 4. x 10 3

3 = 8.15 x 10-5 NOW TRY THIS! 1. Write the following numbers in scientific nottion: b c. 5. d e Write the following s ordinry numbers:. 4 x 10. b. 5.5 x c x d. 8 x e. 4.5 x Prefixes In the SI system, prefixes re used to show multiples nd sub-multiples of units. Multiples: Nme Prefix Multiple kilo K 1000 = 1 X10 3 meg M 1 X 10 6 gig G 1 X 10 9 ter T 1 X 10 1 pet P 1 X

4 Sub-multiples: Nme Prefix Multiple milli m = 1 X10-3 micro 1 X 10-6 nno n 1 X 10-9 pico p 1 X 10-1 femto f 1 X EXMPLES:. Energy stored in chocolte br = J = 1 MJ b. Wvelength of n X ry = m = 1 nm NOW TRY THIS! 1. Rewrite ech of the following quntities using suitble prefix: J b g c s d N e m 4

5 Significnt Figures ll the figures in mesured number re clled significnt figures. The following rules cn be used to determine the number of significnt figures in mesured number: Significnt figures re:. ll nonzero digits e.g cm 4 s.f. 4.5 g 3 s.f. b. zeros between or fter e.g. 305 m 3 s.f. other digits in deciml s.f. number 4.0 kg s.f. Zeros re not significnt if they occur c. in front of number e.g kg 1 s.f. d. in lrge numbers tht m s.f. hve no deciml points 3 s.f. s.f. 1 s.f x x x or 1.7 x10 00 or x 10 NOW TRY THIS! 1. Stte the number of significnt figures in ech of the following quntities:. 4.5 m b

6 c l d mm e. 805 V.. f km Rounding off If the first number to be dropped is. less thn 5, it nd ll following numbers re simply dropped b. 5 or greter, the preceding digit is incresed by 1. EXMPLE 3 s.f. s.f rounds to rounds to NOW TRY THIS! 1. Express the following quntities to 3 sig. figs.: 1055 N; 3.75 m; ; ½ km;.011x10 11 P;. Round off ech of the following numbers to the number of significnt figures indicted: 3 s.f. s.f b c d e

7 Rerrnging equtions The mthemticl reltionships between quntities (the vribles of the eqution) will hold true provided we pply the sme opertions to ech side of the equls sign. If we do the sme thing on ech side, then ech side is still equl to the other. Equtions lwys contin n equls sign. 1. Exmple You cn rerrnge n eqution b c with b s the subject b c or c s the subject c b ny of these three symbols, b, c cn be itself summtion, subtrction, multipliction, division, or combintion of ll. So, when you see more complicted eqution, try to identify its three individul prts, b, c before you strt rerrnging it. Worked exmples Eqution First Rerrngement Second Rerrngement v f f v 1 1 T 1 T f f f T v f 7

8 NOW TRY THIS! From now on the multipliction sign will not be shown, so written s bc b c will be simply omplete the following tble. Eqution First Rerrngement Second Rerrngement (resistnce) V R I= V= I (current) Q I Q = t= t (power) P VI V= I= (power) P I R I = I= R= (power) V P R V = V= R= (resistnce) l R ρ= l= = (Young s interference) (quntum energy) E hf x λ= = = f h (electron wvelength) h mv m= v= 8

9 . Exmple. y + = b Find y in the bove eqution. Since is dded to y, we need to subtrct from both sides to leve y lone on the left-hnd side of the eqution. y subtrcting from both sides we obtin y + = b giving y =b- b. We usully wnt the vrible we re looking for to be on the left-hnd side of the eqution, so you my need to swp sides. p = 4c +3b Rerrnge the bove eqution for b. 4c+3b=p swp the two sides 4c +3b 4c = p 4c subtrct 4c from both sides 3b = p 4c cncel where needed p 4c Finlly: b 3 NOW TRY THIS! Internl resistnce: ε = V + Ir Photoelectric effect hf E k V= I= r= f= Φ= E k = Mnipulting rtios These re the most useful wys of mnipulting rtios. They will help you when you rerrnge equtions. First: 9

10 10 Second: Third: Fourth: nd finlly, this is how you simplify complex frction: c b d d c b It is lwys useful to convert complex frction into simple one, using the form bove, before you try nything else. If b or d re missing, substitute them with number 1. NOW TRY THIS! Here re some exmples to do: [6]

11 Grphs Grphs re very importnt in physics becuse they show ptterns between vribles. For exmple, stright line grph tht strts from the (0,0) point is the best proof tht two vribles re directly proportionl. Stright line grph stright line grph cn be written s y = mx + c where y is the vrible plotted on the y - xis, x is the vrible plotted on the x-xis, m is the grdient of the line nd c is the intercept of the line with the y-xis. The point where the line crosses the y-xis is clled the y-intercept. Plotting grphs: rules lwys drw lrge grph, more thn hlf the size of your grph pper. If you plot grph smller thn this you reduce ccurcy; the lrger the grph, the more ccurte your plot. Pick sensible scle for your xes. Ensure you cn include the lrgest vlue of the vrible to be plotted. Use 1,, 4, 5 or 10 squres for ech increse on the xis; these re esy to use when plotting deciml vlues between whole numbers. Never use 3 or 7 squres wkwrd to use nd will lose mrks in n exm. lwys lbel ech xis with the vrible nd the unit of mesurement. Plot points crefully. If stright line is expected, or suspected, drw best fit line through your points using ruler. 11

12 NOW TRY THIS! 1. Find the grdient of the grph nd the intercept on the y xis: Grdient = Intercept=.n experiment on fixed resistor gve the following vlues of current I (mps) t vrious voltges V (volts): V /V I / m Plot grph of I (y xis) ginst V (x xis). rw line of best fit nd clculte (i) The grdient of the grph (ii) The intercept on the y xis 1

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