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 10. (6.02 x 1023) (–5.11 x 10–27) 8.9 x 108 –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 12. (8.2 x 10–3) (–7.9 x 107) 4.2 x 10–6 7.3 x 10–16
6. 7.85 x 1026 13. (–1.6 x 105) (–2.4 x 1015) 6.02 x 1023 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. y is proportional to x ______ii. y is proportional to the square of x ______iii. y is inversely proportional to x______
11. 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 = ______
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 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 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 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