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Introduction to Measurement
Exactly how “good” is a measured number?
PRE-LAB ASSIGNMENTS:
Before doing this lab you should have completed the following prelab tutorials or taken the
corresponding fast-track quizzes demonstrating your proficiency.
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Measurements and Units
Significant Figures
STUDENT LEARNING OUTCOMES:
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Become familiar with some basic measurement devices.
Recognize that measurements made from the same device are not identical (have some
uncertainty.
Recognize that there are actions that we can take to make sure the measurements that we
make will be more reproducible (precise) and have the potential of providing more useful
information.
Define accuracy and precision. Understand that when applied to measurements, these
terms ar relative, not absolute descriptors.
Learn how to properly make and record measurements acquired with both analog and
digital measurement devices with the maximum precision.
The rules for the use and importance of significant figures.
EXPERIMENTAL GOALS:
In this experiment, several measurements of the same entity will be made independently by
individuals in groups of 4 or 5 students and then the results will be compared to determine how
reproducible the measurement was and try to determine specific causes that contributed to the
differences and propose improved procedures for making future measurements. The average
mass of several coins will be determined to gain an understanding of how significant figures are
carried though a calculation.
INTRODUCTION:
Measurements are important in all areas of our lives. A great deal of effort goes into
making sure that the measurements we base our decisions on are accurate, but much of that effort
is hidden from our day-to-day experience.
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What are some measurements made by you or others that affect you as a consumer?
What are some measurements that would be made by someone in a profession that you are
interested in pursuing? In both of these cases, what might the consequences be if those
measurements are off by 5%, 10 % or 25%?
In this lab, you will develop skills for measuring and recording measurements with the
maximum attainable precision, distinguish between accuracy and precision, and develop some
insight into what is required to make measurements that are truly accurate and precise. You will
also learn some tools for gauging the precision (and to a lesser extent, the accuracy) of a
measurement.
In future labs, you will make choices about how you will make measurements that
could affect the quality of your results. Make sure you use this lab to gain better insight
into making quality measurements and recording them correctly.
Measuring Lengths
Measuring Volumes
Measuring Masses
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PROCEDURE:
The goals of following procedures are to:
1. learn to identify sources of error in the measurements you make
2. be able to analyze their cause and devise means to minimize them
3. be able to characterize and report the uncertainty of your measurements
As a result, we want to have real variations and errors in our measurements. The object is not to
get good or perfect data, but to identify sources of uncertainty or error.
Making Independent Measurements
It is important that these measurements be made as independently as possible. Do not watch
other members in your group make their measurements and do not share results until all
members have made a particular measurement.
Describing Sources of Measurement
When analyzing errors, the measurement procedure should be considered carefully and specific
sources of error should be hypothesized. To be of any use, a hypothesis must be specific enough
to be testable. A useful hypothetical source of error should provide enough information about
the procedure to suggest possible ways of improving it or clearly define limitations of the
method so that absolute error limits can be identified.
Example: A driver gets a speeding ticket for going 61 mph in a 55 mph zone even though the
driver was sure that the speedometer read 55 mph. It is decided that the problem must be
identified and fixed in order to prevent future speeding tickets.
Insufficiently specific hypotheses:
The speedometer could be off or the driver could have read the speedometer wrong.
This is the same as saying that there was either an operator error or an instrument
error. Descriptions of this sort, though true, are obvious and offer very little useful
information. Such descriptions will NOT be given credit on a lab report.
More specific hypotheses
- The speedometer may be reading incorrectly because the size of the tires have changed.
- The speedometer is pulsing, indicating a problem with the cable that might result in a low
speed reading.
- The driver was very tall, maybe height might affect the measurement.
- Maybe the driver was far sighted and could not see the speedometer.
- Maybe the driver was leaning to the left or right of center when they read the speedometer.
- Maybe the driver inadvertently sped up after last checking speed.
Observations of this sort should have some basis on observed reality: you would not want to
make the third hypothesis unless the driver was actually tall.
Throughout the experiment, you will work in groups of four (or five).
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A. Measuring the diameter of a coin with a ruler.
Each group is to select one nickel from those available near your assigned balance. Using the
provided ruler, each student in the group should independently measure the diameter of the
nickel. Once all students have measured the nickel, share data and answer the questions in the
data section.
B. Devise and Test Procedure for Determining a Coin’s Diameter
Use another coin (different denomination) to test your method. Independently measure the
diameter of this coin, only comparing results after all persons have measured the coin.
C. Measuring the Mass of a Nickel
General procedure for weighing a sample.
Important: in order to avoid corrosion of the balance, samples (especially chemical reagents)
should never be weighed directly on the balance. We will describe two methods for weighing a
sample indirectly.
The general approach for weighing an item (such as a chemical sample and its container) is as
follows.
1. Confirm that the balance scale is displaying the correct unit (g).
2. Zero the balance and confirm that the mass reading is acceptably close to zero
(typically 0.000 g for the balances we will use) and stable.
3. Place your item on the balance, let the balance stabilize and then record mass with as many
digits as the measurement allows.
4. Remove the item from the balance and insure that the balance returns to zero within
acceptable limits. Failure to do so may indicate improper zero or drift in the balance and
it may be necessary to reweigh the item.
Weighing samples in chemistry lab
Each person should weigh the same nickel used earlier using both of the following procedures.
All students in a group should use the same balance. Measurements should be made
independently and then compared only after all group members have made their measurements.
After all measurements are made compare results and answer the questions on the data sheet.
Method 1 - Weighing by Difference
This method gives the most precise results. The container is weighed twice, once with the
sample and once without the sample and the mass of the sample is determined by calculating
the mathematical difference (subtracting) of the two measurements.
a. Weigh a piece of weighing paper on the balance as described above. Record its weight.
b. Weigh the weighing paper and the nickel: after zeroing the balance, first place the paper on
the balance and then put the nickel on the paper. If the nickel were reactive, this
procedure would protect the balance from damage.
c. Report the mass of the nickel as the difference between the two masses.
Method 2 – Weighing by Taring the Container
The balance can be zeroed with a container on it, which allows the mass of the container to
be accounted for without having to do any calculations. This process is known as taring.
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This method does not take into consideration changes in the balance, such as drift, that occur
between taring the container and measuring the sample mass. Therefore this method should
not be used when high accuracy and precision are required.
a. Place the weighing paper on the balance and hit the “Zero” or “Tare” button or bar.
Confirm that the balance reading goes to a value that is sufficiently close to zero for your
application (usually 0.000 g in this lab).
b. Place the nickel on the balance by putting it on top of the weighing paper. Let the scale
stabilize and then read the mass of the nickel directly from the balance scale.
D. Determining the average mass of four nickels.
This exercise will be completed as a group.
There should be 4 nickels located next to each balance. Weigh each nickel individually and the
mass of the 4 nickels together.
E. Reading a Graduated Cylinder
Have one member of your team put an arbitrary amount of water in a graduated cylinder.
Starting with that person, each individual should independently read and record the volume in
the cylinder. After all measurements are made compare results.
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LAB REPORT
Measurements I: Mass, Length and Volume Measurements
Name _________________________
Date _______ Section _______ Report Grade ______
Partner 1 __________________________
Partner 2 __________________________
Partner 3 __________________________
Partner 4 __________________________
A. Diameter of Nickel
SAMPLE ID: Year stamped on nickel? ______________________
Table 1. Diameter of Nickel – 1st Pass
(ALWAYS record all measurements and calculated results with units and correct significant figures.)
My
Measurement
Measurements of other group members
Name
Diameter
Average ___________
Range (highest-lowest) __________
% Range (range/average x 100%) __________
Are there any outliers or trends in the data?
Is their sufficient reason to possibly discard 1 or more points?
Compare the methods used by individuals to explain any variations. If after this discussion, you
feel like there is one or more points that would be best excluded from the data set, discuss that
possibility with your instructor.
Put diagram showing improperly aligned rulers
Proposed Modified Procedure
Based on your observations and discussion, describe briefly a modified procedure that is
designed to obtain more uniform results between individuals.
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B. Diameter of Other coin
Use another coin (different denomination) to test your method. Independently measure the
diameter of this coin, only comparing results after all persons have measured the coin.
SAMPLE ID: Type of coin ____________
Year stamped on coin? ______________
Table 2. Diameter of coin
My
Measurement
Measurements of other group members
Name
Diameter
Average ___________
Range (highest-lowest) __________
% Range (range/average x 100%) __________
Are there any outliers or trends in the data?
Is their sufficient reason to possibly discard 1 or more points?
Did you see an improvement in reproducibility in the measurement?
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C. Measuring the Mass of a Nickel
My Measurements:
Mass by Difference
Mass Using Tare Feature
Mass of paper and nickel
________
Mass of paper
________
Mass of nickel
________
Table 3: Comparison of Masses
Mass by
Student Name
Difference
________
Mass Using
Tare Feature
Average
Range
% Range
Observations and Discussion
D. Determining the average mass of four nickels.
Table 4: Nickel Masses
Date of Nickel
Mass of Nickel
Mass of all four nickels (from summing individual masses) __________
Average mass of a nickel __________
All Nickels
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Calculated Averages and Significant Figures
Sum the masses obtained for each of the four nickels: ______________
Going from left to right, what is the first decimal place in which the sum does not agree with the
measured total mass?
This is the decimal place of the last significant digit in the calculated number.
To determine the number of significant figures in a number that is obtained by addition or
subtraction, the decimal place of the last (rightmost) significant figure in each number is
identified. Of these, the largest is the decimal place of the calculated value.
For example: when 2450 is added to 3700,
Last significant digit in 2450 is 5 (10’s place). Last significant digit in 3700 is 7 (100’s place).
The highest of these is the 100’s place, so . . .
the last significant figure in sum should be in the 100’s place.
2450 + 3700 = 6150 which when rounded to 100’s place gives 6200 (2 sig. figs).
Above we determined the number of significant figures of the sum of nickel masses by
comparing it to the total measured mass. Was that observation consistent with the
addition/subtraction rule just presented?
Consider the situation where you added nickel masses together: how does the number of
significant figures compare to that of the original masses?
Calculate the average mass of the nickels. ________________
To determine the number of significant figures obtained by multiplication and division, the
number of significant figures of each number must be determined. The answer will have the
same number of significant figures as the least of these.
Example: what is the surface area of one side of an index card that is 7.6 cm x 12.7 cm. The
lengths have 2 and 3 significant figures, respectively and the area should have 2 significant
figures.
7.5 cm x 12.7 cm = 95.25 cm2 to 2 sig. fig’s gives 95 cm2.
If a calculated number may be used for future calculations, it is advantageous to report the
correct number of significant figures + 1 extra to avoid round off errors in future calculations.
In this case, we would report 95.3 cm2. The underscore under the 5 indicates that it is the last
significant digit and that the number has 2 significant figures.
The number of nickels used to calculate the average is an exact number and can be considered to
have an infinite number of significant figures. In calculating the average mass of a nickel, we
are dividing the sum of the masses (which has n significant figures) by the number of nickels
(infinite number of significant figures), so the number of significant figures should be the
number of significant figures in the combined masses. How does this number compare with the
number of significant figures in the original mass determinations?
It is common for averages to have more significant digits than the numbers they are averaging.
Does this make practical sense? Explain.
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E.
Reading a Graduated Cylinder
Table 1. Volume of water in graduated cylinder.
My
Measurement
Measurements of other group members
Name
Volume
Average ___________
Range (highest-lowest) __________
% Range (range/average x 100%) __________
Are there any outliers or trends in the data?
Is their sufficient reason to possibly discard 1 or more points?
Compare the methods used by individuals to explain any variations. If after this discussion, you
feel like there is one or more points that would be best excluded from the data set, discuss that
possibility with your instructor.
Based on your observations and discussion, describe briefly a modified procedure that is
designed to obtain more uniform results between individuals.
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QUESTIONS:
1. In grammatically correct sentences, describe one advantage and one disadvantage of
determining mass by the balance taring method compared to obtaining a mass by difference.
Advantage of balance taring:
Disadvantage of balance taring:
2.
3.