Scientific Notation Worksheet

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Name:_____________________________Course: _________________Scientific NotationPart A: Express each of the following in standard form.1. 5.2 x 1035. 3.6 x 1012. 9.65 x 10–46. 6.452 x 1023. 8.5 x 10–27. 8.77 x 10–14. 2.71 x 1048. 6.4 x 10–3Part B: Express each of the following in scientific notation.1. 78,0005. 162. 0.000536. 0.00433. 2507. 0.8754. 2,6878. 0.012654Part C: Use the exponent function on your calculator (EE or EXP) to compute the following.1. (6.02 x 1023) (8.65 x 104)8. (5.4 x 104) (2.2 x 107) 4.5 x 1052. (6.02 x 1023) (9.63 x 10–2)9. (6.02 x 1023) (–1.42 x 10–15) 6.54 x 10–63. 5.6 x 10–1810. (6.02 x 1023) (–5.11 x 10–27) 8.9 x 108 –8.23 x 1054. (–4.12 x 10–4) (7.33 x 1012)11. (3.1 x 1014) (4.4 x 10–12) –6.6 x 10–145. 1.0 x 10–14 12. (8.2 x 10–3) (–7.9 x 107) 4.2 x 10–6 7.3 x 10–166. 7.85 x 102613. (–1.6 x 105) (–2.4 x 1015) 6.02 x 1023 8.9 x 1037. (–3.2 x 10–7) (–8.6 x 10–9)14. (7.0 x 1028) (–3.2 x 10–20) (–6.4 x 1035)Working in Significant FiguresConvert the following: (Maintain 3 significant digits).1.21 m. = _____________________cm.34.5 mm. = _____________________ cm.3.68 cm. = _____________________ m.1.21 μs _____________________ s.1.12 cm2 = _____________________ m21.24 x 10-4 m3 = _____________________cm3Analysis QuestionsIf distance, d, is proportional to time, t, and at time t = 2.00 seconds, the distance is 6.20 m, find the distance when t = 3.50 s. _____________________If acceleration, a, is inversely proportional to mass, m, and when the mass is 4.50 kg the acceleration is found to be 2.00 m/s2, find the acceleration when the mass is 18.0 kg. _____________________If the distance traveled, d, is proportional to the square of the time, t, and after 4.00 seconds the distance is 10.0 meters, find the distance after 8.00 seconds. _____________________In the figures above, there are three rough graphs of y vs. x. For each of the following, fill in A, B, or C:y is proportional to x __________y is proportional to the square of x __________y is inversely proportional to x__________685800-952500The right triangle to the left has legs, O and A, and hypotenuse H. One of its acute angles is θ. Solve the following problems (maintain 3 sig figs):A = 10.0, θ = 30.0o, O = __________O = 10.0, θ = 37.0o, H = __________O = 10.0, A = 20.0, θ = __________There are two rules for determining the number of significant figures:1) If there is no decimal point--start at the RIGHT and count, beginning with the first non-zero digit.Examples 340 2 s.f.30400 3 s.f.34955 5 s.f.2) If there is a decimal point--start at the LEFT and count, beginning with the first non-zero digit.Examples 340. 3 s.f.30400. 5 s.f.0.34955 5 s.f.0.00040 2 s.f.Determine the number of significant figures (s.f.) in each of the following:a) 921 ______b) 92100 ______c) 92100. ______d) 0.000210______e) 0.00219 ______f) 93,000,000 ______g) 93,000,003 ______h) 93,000,000.______There are also rules for reporting numbers when you multiply and/or divide:1) Count the sig. figs. in the numbers you are multiplying and/or dividing. Your answer should berounded off to the smallest number of sig. figs. in your problem.Example: a) 28.33 x 3.12 = “88.3896” ?-----calculator answer???????????????????????? 4 s.f. 3 s.f. 6 s.f. So round to 3 s.f., your answer will be reported as 88.4b) 28.44 ??3.12 = “9.080128205” ?-----calculator answer?????????????????4 s.f. 3 s.f. 6 s.f. So round to 3 s.f., your answer will be reported as 9.08Reminder: Rounding-off rules: Go to next number. If it is 0-4, round down. If it is 5-9, round up.Report the answer to the following problems, paying particular attention to the correct number of sig. figs.a) 986.72 / 5.12 = ______b) 497.7 / 3.0 =______c) 920.7 / 4.32 = ______d) 400.20 x 3.010 =______e) 98 x 0.006 = ______f) .009430 x 4310.9 =______g) 45.20 x 0.0071 = ______h) 9.0 / 3.0 =______i) 10. x 300. = ______j) 10. / 3 =______There are also different rules for reporting the answer when you add or subtract:1) The answer should have the same number of decimal places as that of the number with the leastdecimal.Example: 4.838 g 486.58 g+1.0023 g - 421. g_5.3853 g = 5.385 g 65.58 g = 66 g??????????????????is 0-4, so round down. is 5-9, so round up.NOTE: IN ADDITION AND SUBTRACTION, DECIMAL POINTS MUST BE LINED UP!!Solve the following:a) 0.00000313 b) 4.9670 c) 0.000343 d) 78 + 17 - 3.1 ___ +0.17 - .99e) 336,000 – 33,000.03 = f) 0.99 - .1 = ______ Additional practice problems:How many sig. figs in the following number?a) 87_____ b) 190._____ c) 0.000190_____ d) 606.0_____ e) 1.008_____Round off the following to 2 S.F.a) 86730__________ b) 120.99__________ c) .0003450_________ d) 0.0555_________ e) 9898989________How many S.F. should be in the following answers: (Don’t work out the problems!)a) 0.2 x 43.98 = _____ b) 43,000,000 x 0.00546 = _____ c) 43.0 – 17.2 = _____d) 0.00235 – 3.0 = _____ e) 143.000 – 3.45 = _____ f) 3.40 x 0.04 = _____g) 0.300 x .802 = _____ h) 39.04 x 1.009 = _____ i) 0.00390 x 2.0098 = ____30.44 3 2.02Solve the following problems:a) 0.004598 b) 43.2 x 30.3 x 17.0 = c) 338855.0 + 4______ 43.30 x 0.0045 x 99 + 10000000.003d) 73 e) 8.0 f) 17.0 + 1.4 – 8.9 = ________ -14.98 -1.99How many S.F. are in the following numbers?a) 3.0 x 109 _____ b) 0.0090 _____ c) 4.20 x 10-4_____d) 900,000_____ e) 900,000._____ f) 9.4450 x 107_____Converting English and Metric1 ) 8.5 inches = _________ centimeters2 ) _________ cubic feet = 3.5 cubic meters3 ) 6 square feet = _________ square meters4 ) 17.5 square yards = _________ square meters5 ) _________ gallons = 9 liters6 ) 15.5 yards = _________ meters7 ) _________ inches = 19 centimeters8 ) _________ cubic inches = 4.5 milliliters9 ) 20.5 square inches = _________ square centimeters10 ) _________ square inches = 9.5 square centimeters11 ) 5.5 mph = _________ kmph12 ) 7 feet = _________ meters13 ) _________ miles = 5 kilometers14 ) 11 mph = _________ kmph15 ) 12.5 cubic feet = _________ cubic meters16 ) _________ cubic yards = 19.5 cubic meters17 ) _________ gallons = 13.5 liters18 ) _________ miles = 1.5 kilometers19 ) 25 feet = _________ meters20 ) _________ square yards = 4 square meters ................
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