Physics 521. Math Review SCIENTIFIC NOTATION SIGNIFICANT FIGURES. Rules for Significant Figures

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Kathlyn Franklin
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1 Physics 51 Math Review SCIENIFIC NOAION Scientific Notation is based on exponential notation (whee decimal places ae expessed as a powe of 10). he numeical pat of the measuement is expessed as a numbe between 1 and 10 multiplied by a whole-numbe powe of 10. M * 10 n, 1 M < 10, whee n is an intege (+ o - #). Standad Notation 000 * 10 3 Standad Notation 180 g 1.8 * 10 g o 1.8 * 10-1 kg SIGNIFICAN FIGURES Significant Figues - he numbe of digits is ough but useful indication of a measuements pecision. Each digit obtained as a esult of measuement is a significant figue. he last digit of each measued quantity is always estimated. he zeos in a numbe waant special attention. A zeo that is the esult of a measuement is significant, but zeos that seve only to mak a decimal point ae not significant. A) 65 ml ( sig figs) B) (4 sig figs) C) 13. g (3 sig figs) D) 5 ml (1 sig figs) Rules fo Significant Figues 1. Non-zeo digits ae always significant. Ex. A) 34.7 L (4 sig figs) B) 1.91 kg (4 sig figs). A zeo between othe SF is significant. Ex. A) 1.05 (3 sig figs) B) 001 m (4 sig figs) 3. Final zeos to the ight of the decimal point ae significant Ex. A) 6.30 g (3 sig figs) B) ml (4 sig figs) 4. Initial zeos ae not significant and seve only to show place of decimal. Ex. A) km ( sig figs) B) (3 sig figs)

2 5.Final zeos in numbes with no decimal point may o may not be significant. A) 0 mables *count, exact, infinite* B) 000 m *1* C) 0 lbs *1* pecise fom D).0 x 10¹ lbs ** pecise fom E).00 x 10¹ lbs *3* pecise fom Intepetations of Significant Figues 00 lbs *1* significant figues... bette witten * 10 lbs 00 lbs ** significant figues... bette witten.0 * 10 lbs 00 lbs *3* significant figues... bette witten.00 * 10 lbs F) 1 km 1000 m *definition, infinite* COUNS, CONSANS, DEFINIIONS All have an infinite numbe of significant figues.( ) COUN - Ex. 10 mables, 3 people... Exact SIGNIFICAN FIGURE CALCULAIONS he esult of any mathematical calculation involving measuements cannot be moe pecise than the least pecise measuement. (Assume all the numbes below ae fom a measuing) CONSANS - Ex. Conside a + b c. he numbe is a constant. DEFINIIONS - Ex. 1 km 1000 m, 1 1 dozen Addition and Subtaction When adding o subtacting measued quantities, the answe should be expessed to the same numbe of decimal places as the least pecise quantity used in the calculation. ( If needed use a LINE OF SIGNIFICANCE to aid in solving these.) A) B) C) D) E) * 10 3 F) * 10 3 Multiplication, Division, and Squae Root When multiplying, dividing, o finding the squae oot of measued quantities, the answe should have the same numbe of significant digits as the least pecise quantity used in the calculation. A) * B) 500 * 5000 C) 6.3 *

3 ROUNDING When completing calculations, do not ound any of the intemediate answes on you way to finding a solution to a poblem. he only ounding that should occu is in the final answe that is being epoted. ( )( ) ( )( ) INVERSELY AND DIRECLY PROPORIONAL When consideing what effect changing one o moe vaiables has on anothe vaiable in mathematical elationships invesely and diectly popotional elationships ae used. C A, AB C D C A, o C A, if C doubles then A doubles Now, at the vey end ound to 1 sig fig Answe is 1 C 1/D D C, o D C, if D doubles then C becomes half Diectly Popotional Quantities Invesely Popotional Quantities Quantities that ae diectly popotional to one anothe incease o decease by the same facto. Quantities that ae diectly popotional to one anothe occupy the same position on opposite sides of the popotion sign (eithe both located in the numeato position o both in the denominato position). AX ZP Z & X ae diectly popotional to each othe. ( Z α X ) Quantities that ae invesely popotional to one anothe change by the ecipocal of one anothe (o 1/x of one anothe). In a popotion, quantities that ae invesely popotional to one anothe occupy opposite positions on opposite sides of the popotion sign. Z X N M Z & M ae invesely popotional to each othe. ( Z α 1/M) Given the following fomula, what would happen to v if is doubled and is tipled? π v Answe: v would change by a facto of, v 3 Given the following fomula, what would happen to m c if is changed by a facto of and G by a facto of ½? Answe: v would change by a facto of, 3 Gm c 1 m c

4 Unit Analysis Often we need to change the units in which a physical quantity is expessed. Fo example we may need to change seconds and minutes, hous, days o even yeas, to do this we use convesion factos. 60sec 1 1min and 1min 60sec 1 When a quantity is multiplied by convesion facto it does not change the amount of quantity just the units the quantity is measued in. When a convesion facto is evaluated its value is equal to 1. Any numbe multiplied by 1 emains unchanged. 180sec 1 1min 180sec 60sec Second ae cancelled which leaves units of minutes Answe: (3 min) How many centimetes ae in 1 km? How many seconds ae in one day? 1000m 100cm 1 km? 1km 1m 1*10 5 cm 4h 60 min 60sec 1 day? 1day 1h 1min sec Convet.4 km/h to m/s km 1h 1min 1000m.4? h 60 min 60sec 1km he metic system Pefix Symbol Facto 1 tea giga G mega M kilo k hecto h deca da base unit base unit deci d m/s 1 centi c milli m mico : nano n pico p femto f atto a

5 Solve fo q: Re-aanging fomulas Given the following fomula, q E k Given the following fomula, Solve fo : ac E q k a c Given the following fomula, ( ) d 1 v f + vi t Solve fo v f : d v f vi t

Motithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100

Motithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100 Motithang Highe Seconday School Thimphu Thomde Mid Tem Examination 016 Subject: Mathematics Full Maks: 100 Class: IX Witing Time: 3 Hous Read the following instuctions caefully In this pape, thee ae thee