Practice Questions
Measurements and Data Analysis
1. Write each of the following numbers in scientific notation
a) 27600
b) 0.00045
c) 538000
d) 0.39x10-5
e) 84x10-3
f) 297x103
g) 0.043x10-6
h) 0.689x1024
i) 860.3x10-19
j) 0.00000007936
2. Express each of the following in scientific notation in the basic SI unit
a) 5.00x106 mm
b) 6.000 km
c) 25 nm
d) 55.00 min
e) 3.6 hrs
f) 37 g
g) 1500 kg
3. Perform the following mathematical operations, expressing the answers to
the correct number of significant digits
a) 463.66 +29.2 + 0.17
b) 426.66-39.2
c) (2.6)(42.2)
d) (65)(0.041)(325)
e) (0.0060)(26)(55.1)
f) (650)/(4.0)
g) (0.452)/(0.012)
h) (3.5)2
i) (5.89x102)(3.4x105)(1.44x10-3)
j) (6.789x1013)/(6.94x108)
k) (3.854x105)/(9.424x10-8)
l) 8.54x102 + 3.83x103 + 5.4x102)
4. Calcuate the area of a rectangle that has a width of 12.45m and a length
of 32m.
5. An cast iron cannon ball has a radius of 10cm and a mass of 15.5kg.
Determine the density of cast iron.(density=mass/volume)
6. A flag pole is made by connecting three individual section. If the
lengths of the sections are 5.4m, 2.25m and 0.756m, then what is the height
of the pole?
7. Three steel strips have the following dimensions:
strip 1 l = 148.2 cm w = 3.0 cm
strip 2 l = 102 cm w = 1.29 cm
strip 3 l = 142.73 cm w = 5.891 cm
Calculate the following and express the result to the right number of
significant digits using scientific notation.
a) the total length of the strips joined end to end
b) the total width of the strips joined side to side
c) the area of each of the strips
d) the ratio of l/w for each of the strips
8. A student measures the acceleration due to gravity and finds it to be
9.72m/s2. What is the percentage error, if the accepted value is
9.81m/s2
9. The maximum possible error on an electronic balance during a measurement
is 0.01g. What is the percentage error for each of the following
measurement?
a) 700g b) 20g c) 3kg d) 1g
10. A student measures Planck's constant twice. The first measurement
produces a value of 5.78x10-34 J.s , and the second measurement
produces a value of 7.29x10-34 J.s. If the accepted value is
6.63x10-34 J.s, what is
a) the percentage difference for the measured values?
b) the percentage error for each value?
11. Write a proportionality statement and determine the equation for each of
the following sets of values
A |
B |
2 |
100 |
8 |
200 |
50 |
500 |
200 |
1000 |
|
|
C |
D |
3 |
120 |
6 |
60 |
9 |
40 |
12 |
30 |
|
|
E |
F |
2 |
90 |
16 |
180 |
54 |
270 |
250 |
450 |
|
|
G |
H |
6 |
5 |
12 |
20 |
18 |
45 |
45 |
245 |
|
|
K |
L |
7 |
800 |
28 |
50 |
35 |
32 |
70 |
8 |
|
|
|
|
12. Given that the kinetic entergy Ek=[mv2]/2, by what
factor will Ek change by if the following changes are made.
a) the mass is doubled
b) the mass is decreased by a factor or 3
c) the velocity is doubled
d) the velocity is decreased by a factor of 4
e) the mass is increased by a factor of 5 and the velocity is decreased by a
factor of 2
f) the mass is decreased by a factor of 50 and the velocity is increased by
a factor of 2.5
13. Given that d is proportional to at2.
If a=2.0m/s2 and t=4.0s when d=32m, what will be the value of d
when a=4.0m/s2 and t=12s?
14. For the following three sets of experimental data find the
relationship(the equation) between each pair of variables using
a) the log method
b) the linearization method
v |
F |
20 |
10 |
28 |
20 |
40 |
40 |
48 |
60 |
|
|
R |
F |
0.1 |
1.0 |
0.2 |
0.25 |
0.3 |
0.11 |
0.4 |
0.04 |
|
|
T |
R |
7.6x106 |
5.8x1010 |
30x106 |
15x1010 |
380x106 |
78x1010 |
930x106 |
143x1010 |
|
|
|