Review
Phy 122L/132L/123L/133L
Name: ______________
Significant Digits, Unit Conversions, Graphing and Uncertainties in Measurements
===========================================================
Choose the best answer.
(30 pts total)
1. What is the “most significant digit” (MSD) in 0.01357?
a. 0
b. 3
c. 5
d. 7
e. 1
2. What is the “least significant digit” (LSD) in 3260?
a. 2
b. 3
c. 6
d. 0
e. It is ambiguous. You don’t know if the “0” is merely a placeholder or significant.
3. What is the “least significant digit” (LSD) in 2.40 x 10-5?
a. 4
b. 2
c. 0
d. 10-5
e -5
Do the following calculations and express the result in scientific notation with the correct
number of significant digits:
4.
36.94 - 25.2 + 100.81 = ???
a. 112.55
d. 1.126 x 102
b. 112.6
e. 1.126 x 10-2
2
c. 1.1255 x 10
Use the “multiply by one in the form of” method to convert the following expressions. Express
the final answer in scientific notation with the correct number of significant digits and units.
5. Express 3300 g/cm3 in kg/m3.
a. 3.3 x 102 kg/m3
b. 3.300 x 102 kg/m3
c. 3.3 x 103 kg/m3
d. 3.3 x 106 kg/m3
6. When drawing a graph, it is best to draw it small, so it takes only a small part of the graph
paper and the data points are close to each other.
a. True
b. False
7. Titles for your graphs …
a. are not always necessary.
b. can be written with symbols/variables only.
c. are a word description that describes what is in your graph and are always required.
8. Do not mix units in a graph or they won’t cancel properly in the slope (Δy/Δx). Use the same
type of units for the same type of number on both axes. Which of the following sets of units
is NOT ok to use?
[Remember: N = kg m/s2]
a. y-axis = N and x-axis = m/s2
b. y-axis = g cm/s2 and x-axis = cm/s2
c. y-axis = N and and x-axis = cm/s2
CSU Pomona
Updated 1/08/12
Dr. Julie J. Nazareth
Review
Phy 122L/132L/123L/133L
9. Which of the following should you include in the axes labels of your graphs?
a. units
d. Answers a & b
b. symbol/variable for what is being plotted
e. Answers a, b & c
c. word description of what is being plotted
10. Which of the following is the “best” fit line?
a.
b.
c.
d.
11. When it is acceptable to use a data point as a slope point?
a. if the data point appears to fall upon the line
b. if the data point appears to fall upon the line and if it falls at the extreme end of the page
c. NEVER, because this tends to influence the positioning of the “best” fit line.
12. To minimize uncertainty in a graph the two slope points should be (as much as reasonably
possible) which of the following?
a. at extreme ends of the page of paper
c. at the intersection of the grid lines
b. never a data point
d. All of the above
13. Which is the incorrect formula for calculating the slope (Δy/Δx) with the slope points
(x1, y1) and (x2, y2)?
a. (y1 – y2) / (x1 – x2)
b. (y2 – y1) / (x2 – x1)
c. (y1 – y2) / (x2 – x1)
CSU Pomona
Updated 1/08/12
Dr. Julie J. Nazareth
Review
Phy 122L/132L/123L/133L
14. How should you find the y-intercept of your graph? (Remember, choose the best answer.)
a. Measure the y-value off your graph where the x-value is 0.
b. Use the equation of a line to solve for the y-intercept algebraically.
c. Answer b always works, but answer a works only if the graph includes the origin.
You are using a ruler to measure lengths. Assume that you can reasonably measure to onehalf of the smallest division. This means you can see if the length of the object is closer to
one of the tick marks, half-way between two tick marks, or closer to the following tick
mark. (If you can’t tell if a measurement is closer to a tick mark or half-way in between,
then you can only reasonably measure to the nearest whole of the smallest division). This is
your instrumental precision (instrumental uncertainty).
15. If the smallest division on your ruler is 1 mm (= 0.1 cm), what is the numerical value of your
instrumental precision (instrumental uncertainty)?
a. 1 mm
b. 0.1 cm
c. 0.05 cm
d. 0.05 mm
16. If a rod is exactly three centimeters long, how would you record the length to reflect the
precision of the instrument (and therefore, how well you can measure the length)?
a. 30 mm
b. 3.0 cm
c. 3.00 cm
d. 30.00 cm
Questions 17-18: A student made the following six measurements of the mass of an object:
m = 56.6 g, 56.6 g, 56.6 g, 56.6 g, 56.6g, 56.6 g. The instrumental uncertainty is δinst = 0.1 g.
17. What is a reasonable estimate of the sample uncertainty, δsamp?
a. 0.0 g
b. 0.1 g
c. 0.6 g
d. 56.6 g
18. What is a reasonable estimate of the uncertainty of the measurement, δm? To determine
this, look at both the instrumental and sample uncertainties and choose the larger value.
a. 0.0 g
b. 0.1 g
c. 0.6 g
d. 56.6 g
Questions 19-20: A student made the following nine measurements of the wavelength of a
standing wave: l = 14.4 cm, 15.1 cm, 14.2 cm, 14.6 cm, 14.4 cm, 14.8 cm, 13.7 cm, 13.9 cm,
14.9 cm. Assume the instrumental uncertainty is 0.1 cm
19. What is a reasonable estimate of the sample uncertainty, δsamp? (Choose the best answer)
a. 0.1 cm
b. 0.4 cm
c. 0.5 cm
d. 0.7 cm
e. 1 cm
f. Answers c and d are both reasonable estimates.
20. What is the “best estimate” of the true value of the measurement, tbest? In most cases, this is
the average of the measured values. Remember, this value should be rounded to the same
decimal place as the uncertainty, δt.
a. 13.7 cm
b. 14.4 cm
c. 15.1 cm
d. 14 cm
21. A student measures a coefficient of linear expansion of (14.2 ± 0.8)x10-6 C°-1 for a steel tube
and the accepted value for commercially available steel is 11.3 x10-6 C°-1 to 13.5x10-6 C°-1.
How would you describe the two values/numbers?
a. They do not agree. (There is a significant discrepancy.)
b. They are close but do not quite agree. (There is a slightly significant discrepancy.)
c. They agree within uncertainty. (There is no significant discrepancy.)
CSU Pomona
Updated 1/08/12
Dr. Julie J. Nazareth
Review
Phy 122L/132L/123L/133L
Questions 22 & 23: Propagating Uncertainty through a calculation
Follow the outlined steps to perform the following calculations including uncertainty. Write out
your final answer (value with its associated uncertainty) following the Rules for reporting
experimental values (see Appendix C of the Phy 121L/131L lab manual). Reduce rounding error
by keeping at least two extra non-significant digits in intermediate calculations. Show all work.
22. [(34.35 ± 0.05) g – (30.35 ± 0.05) g] (9.80 m/s2) = ???
Step 1: Subtract the values in the square brackets. Use Rule # 1: add absolute uncertainties.
= [(
±
) g] (9.80 m/s2)
Step 2: Use Rule #4 to multiply the result in the square brackets by (9.80 m/s2), a “perfectly
known number.” Remember, for Rule #4, multiply the absolute uncertainty by the
“perfectly known number.” Don’t forget to also multiply the best estimate by the
“perfectly known number”!
= [(
±
) gm/s2]
Step 3 (Last step): Round the absolute uncertainty to one significant digit (or two SD if it the
absolute uncertainty at the conclusion of the previous step begins with a “1” or a “2”)
and round the equation result (best estimate) to the same decimal place.
= [(
±
) gm/s2]
23. [(7.73 ± 0.01) cm] [(19.0 ± 0.1)mm]2 = ???
Give final answer in cm3.
Step 1: Make both length measurements have the same units (mm → cm). Don’t forget to
convert the absolute uncertainty also.
= [(7.73 ± 0.01) cm] [(
±
)cm]2
Step 2: Change the absolute uncertainties into relative uncertainties (as percentages) because
you will need this for both the powers rule #3 (the square) and the multiplication rule #2.
= (7.73 cm ±
%) [(
cm ±
%)]2
Step 3: Do the square. Square the best estimate and use Rule #3 to multiply the power (= 2 in
this case) times the relative uncertainty. Don’t do anything to the 7.73 cm ± relative
uncertainty yet. Just write it down in the calculation
= (7.73 cm ±
%) (
cm2 ±
%)
Step 4: Multiply the best estimate numbers and use Rule #2 to add the relative uncertainties.
=(
cm3 ±
%).
Step 5: Change the relative uncertainty back to absolute uncertainty.
=(
±
) cm3
Step 6 (Last step): Round uncertainty to one significant digit (or two SD if it the absolute
uncertainty at the conclusion of the previous step begins with a “1” or a “2”) and round
the result of the calculation to the same decimal place.
=(
±
) cm3
CSU Pomona
Updated 1/08/12
Dr. Julie J. Nazareth