Assignment
Name: _____________________________ Course: _________________ Scientific Notation Part A: Express each of the following in standard form. 1. 5.2 x 103 5. 3.6 x 101 2. 9.65 x 10–4 6. 6.452 x 102 3. 8.5 x 10–2 7. 8.77 x 10–1 4. 2.71 x 104 8. 6.4 x 10–3 Part B: Express each of the following in scientific notation. 1. 78,000 5. 16 2. 0.00053 6. 0.0043 3. 250 7. 0.875 4. 2,687 8. 0.012654 Part 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 105 2. (6.02 x 1023) (9.63 x 10–2) 9. (6.02 x 1023) (–1.42 x 10–15) 6.54 x 10–6 3. 5.6 x 10–18 8.9 x 108 10. (6.02 x 1023) (–5.11 x 10–27) –8.23 x 105 4. (–4.12 x 10–4) (7.33 x 1012) 11. (3.1 x 1014) (4.4 x 10–12) –6.6 x 10–14 5. 1.0 x 10–14 4.2 x 10–6 12. (8.2 x 10–3) (–7.9 x 107) 7.3 x 10–16 6. 7.85 x 1026 6.02 x 1023 13. (–1.6 x 105) (–2.4 x 1015) 8.9 x 103 7. (–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 Figures Convert the following: (Maintain 3 significant digits). 1. 1.21 m. = _____________________cm. 2. 34.5 mm. = _____________________ cm. 3. 3.68 cm. = _____________________ m. 4. 1.21 μs _____________________ s. 5. 1.12 cm2 = _____________________ m2 6. 1.24 x 10-4 m3 = _____________________cm3 Analysis Questions 7. If 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. _____________________ 8. 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. _____________________ 9. 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. _____________________ 10. In the figures above, there are three rough graphs of y vs. x. For each of the following, fill in A, B, or C: i. ii. iii. y is proportional to x __________ y is proportional to the square of x __________ y is inversely proportional to x__________ 11. iii. The 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): i. A = 10.0, θ = 30.0o, O = __________ ii. 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. 30400. 0.34955 0.00040 3 s.f. 5 s.f. 5 s.f. 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 be rounded 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 88.4 b) 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 9.08 Reminder: 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 least decimal. 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 + 17 b) 4.9670 - 3.1 ___ c) 0.000343 +0.17 e) 336,000 – 33,000.03 = d) 78 - .99 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 = _____ 30.44 h) 39.04 x 1.009 = _____ 3 i) 0.00390 x 2.0098 = ____ 2.02 Solve the following problems: a) 0.004598 b) 43.2 x 30.3 x 17.0 = + 4______ 43.30 x 0.0045 x 99 d) 73 -14.98 e) 8.0 -1.99 c) 338855.0 + 10000000.003 f) 17.0 + 1.4 – 8.9 = ________ How 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 Metric 1) 8.5 inches = _________ centimeters 2) _________ cubic feet = 3.5 cubic meters 3) 6 square feet = _________ square meters 4) 17.5 square yards = _________ square meters 5) _________ gallons = 9 liters 6) 15.5 yards = _________ meters 7) _________ inches = 19 centimeters 8) _________ cubic inches = 4.5 milliliters 9) 20.5 square inches = _________ square centimeters 10 ) _________ square inches = 9.5 square centimeters 11 ) 5.5 mph = _________ kmph 12 ) 7 feet = _________ meters 13 ) _________ miles = 5 kilometers 14 ) 11 mph = _________ kmph 15 ) 12.5 cubic feet = _________ cubic meters 16 ) _________ cubic yards = 19.5 cubic meters 17 ) _________ gallons = 13.5 liters 18 ) _________ miles = 1.5 kilometers 19 ) 25 feet = _________ meters 20 ) _________ square yards = 4 square meters
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