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