Name: Course: Scientific Notation Part A: Express each of the following in standard form. 1. 5.2 x 10 3 5. 3.6 x 10 1 2. 9.65 x 10 4 6. 6.452 x 10 2 3. 8.5 x 10 2 7. 8.77 x 10 1 4. 2.71 x 10 4 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 10 23 ) (8.65 x 10 4 ) 8. (5.4 x 10 4 ) (2.2 x 10 7 ) 4.5 x 10 5 2. (6.02 x 10 23 ) (9.63 x 10 2 ) 9. (6.02 x 10 23 ) ( 1.42 x 10 15 ) 6.54 x 10 6 3. 5.6 x 10 18 10. (6.02 x 10 23 ) ( 5.11 x 10 27 ) 8.9 x 10 8 8.23 x 10 5 4. ( 4.12 x 10 4 ) (7.33 x 10 12 ) 11. (3.1 x 10 14 ) (4.4 x 10 12 ) 6.6 x 10 14 5. 1.0 x 10 14 12. (8.2 x 10 3 ) ( 7.9 x 10 7 ) 4.2 x 10 6 7.3 x 10 16 6. 7.85 x 10 26 13. ( 1.6 x 10 5 ) ( 2.4 x 10 15 ) 6.02 x 10 23 8.9 x 10 3 7. ( 3.2 x 10 7 ) ( 8.6 x 10 9 ) 14. (7.0 x 10 28 ) ( 3.2 x 10 20 ) ( 6.4 x 10 35 )
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 cm 2 = m 2 6. 1.24 x 10-4 m 3 = cm 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/s, 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. oint--start at the LEFT and count, beginning with the first non-zero digit. The right triangle to the left has legs, O and A, and hypotenusee H. One of its acute angles is θ.. Solve the following problems (maintain 3 sig figs): i. A = 10.0, θ = 30.0 o O = ii. O = 10.0, θ = 37.0 o H = o, o, iii. 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 30400 34955 2) If there is Examples 2 s.f. 3 s.f. 5 s.f. a decimal po 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 b) 4.9670 c) 0.000343 d) 78 + 17-3.1 +0.17 -.99 e) 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 2.02 Solve 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 + 10000000.003 d) 73 e) 8.0 f) 17.0 + 1.4 8.9 = -14.98-1.99 How many S.F. are in the following numbers? a) 3.0 x 10 9 b) 0.0090 c) 4.20 x 10-4 d) 900,000 e) 900,000. f) 9.4450 x 10 7
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