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Using a Calculator Do the following calculations by pressing your calculator as few times as possible. 4528 25616 1.105 3.16 10 8.714 10 6 9.54 10 2 5 1.203 10 4 The physics in this course is challenging but 90% of the difficulties arising in solving physics problems come from small math mistakes (what I call little math). When difficulties arise the first thing to do is look over every step of your calculation or have someone else look it over. SIGNIFICANT DIGITS Two types of quantities are used in science: exact values and measurements. Exact values include defined quantities (1 kg is 1000 g) and counted values ( 12 donuts). Measurements are not exact because they always include some degree of uncertainty. A measurement is made up of numbers that are certain and one digit, the last one that is estimated or uncertain. Digits that are part of the measurement are significant while digits that are not part of the measurement are insignificant. A few rules will help distinguish this statement. •all non-zero digits and in-between zeroes are significant •zeroes in front of all of the non-zero digits are insignificant •zeroes behind all of the non-zero digits and behind the decimal point are significant •zeroes behind all of the non-zero digits but before the decimal may be significant or insignificant (assume insignificant unless you know where the estimated value of the measurement actually is) -use scientific notation to show how many significant digits are present 40025 4.0025 x 104 5 360.20 3.6020 x 102 5 0.00450 4.50 x 10-3 3 2600 2.6 x 103 2 2600.0 2.6000 x 103 5 850000 8.5 x 105 2 12401 1.2401 x 104 5 0.00007 7 x 10-5 1 Calculations and Significant Figures Performing the actual calculation and tracking significant figures is the only real way to ascertain the number of significant figures that make up the correct answer. Whenever an estimated value is part of a calculation the number it produces is estimated. Simplified rules have been developed to make these calculations easier. Adding and Subtracting When adding and subtracting, the answer should be precise to the same number column as the most imprecise number in the calculation. Multiplying and Dividing When multiplying and dividing, the answer should have the same number of significant digits as the number in the calculation which has the fewest significant digits. 105.7 86.84 18.86 18.9 23.45 1147 571.5 1741.95 1742 56.3 2 .9 163.27 160 The rules and procedures you have seen apply to measured values. They will be utilized in lab write-ups or in other lab based evaluations where indicated. On tests, quizzes or assignments you are expected to use 4 significant figures and only 4 significant figures. You may use less if the calculation yields an answer with less than four. examples 2.39 on calculator could be written 2.39 or 2.390 on test 5.9 on calculator could be written 5.9, 5.90 or 5.900 on test 6.00042 on calculator must be written 6.000 on test homework: complete significant figures worksheet UNIT CONVERSION The metric system will be used in this unit so conversions with prefixes will be performed. The units of time also often need to be converted. km 20km 20 1000m 20 ? hr 1hr 3600s 9 nm 50nm 50 110 m 50 2 ? 2 3 2 ms 1ms (110 s) Convert the following measurements to the units stated. -express answer in scientific notation -express answer to 4 significant digits (round properly) a) 6.42 km to m c) 52.3 km/hr to m/s e) 45.9 nm to km g) 45.6 km/hr2 to m/s2 b) 1478 s to hr d) 34.5 Mm to mm f) 79 m/s to km/hr h) 0.239 m/s2 to km/hr2 homework: p.349 6, 8, 9 and worksheets Answers a) 6.420 x 103 m b) 4.106 x 10-1 hr c) 1.453 x 101 m/s d) 3.450 x 1013 mm e) 4.59 x 10-11 km f) 2.844 x 102 km/hr g) 3.519 x 10-3 m/s2 h) 3.097 x 103 km/hr2 REARRANGING EQUATIONS Rearrange the following equations so that the letter indicated is isolated on the left hand side of the equals symbol. v2 v1 at v2 v1 at v2 v1 t a t v2 v1 t a 7 homework p.349 7 n a) A LW W g) V V n 1 2 t b) P 2L 2W W n h) V V t 1 2 2 r t c) A r Gm m 1 2 d d) y mx b x i) F 2 d e) E I 2 RT R v v 1 2 j) d ( )t f) C A(r 2r ) r2 2 1 2 v2