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Scientific Measurement and the Metric
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Purpose In
this experiment we will consider standards of measurement used in science,
especially the metric system, and some elementary mathematical techniques
which enable us to express these measurements in the most convenient form. In this activity we will familiarize
ourselves with the metric system of measurement, metric conversions and the
process of making scientific measurements. |
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Introduction Measurement
is important in science for two reasons, first it is a direct observation or a
statement of fact, and second, a measurement, by its very nature tends to be
an objective observation rather than a subjective observation. Objective observations are verifiable and
not subject to personal bias. Thus,
objective, quantitative measurements are the preferred mode of making
scientific observations. An example of
an objective observation would be the length of the textbook being measured
with a ruler. A subjective observation
would be to estimate the length of the textbook based solely on visual
examination. Another example would be
the determination of temperature. An
objective observation would be to measure the temperature with a thermometer. A subjective evaluation would be to
determine whether an object is "hot" or "cold" be touch. Obviously what is "hot" or
"cold" to one person is not necessarily the same to another. Measurement
is the comparison of a physical quantity of a sample with a selected
standard. By "comparison" we
mean the act of examining two objects side by side, for example a ruler and a
textbook. The "physical quantity
of a sample" means the thing or object we wish to measure, e.g. the
textbook; the "selected standard" is the ruler. The ruler has a series of marks placed upon
it that most people agree conforms or meets a certain measurement. This determination of "how many"
of these "marks" is the process of measurement. Most measurements that are used in commerce
or trade are standardized back to a set of standard weights and measures held
by the Bureau of Weights and Measures of the Precise
measurement lies at the very heart of the scientific enterprise. When we express concepts with words alone,
they may lead to confusion. How big is
"big'?". . . or "small?" How hot
is "hot?" What is "heavy'?" Words often convey different
meanings to different people. Even in
everyday life we express concepts more meaningfully in numbers. We speak of a 3" x 5" file card,
a length of 2" x 4" lumber, a car which averages 16 miles to the
gallon, a temperature of 72ºF, a relative humidity of 65%, a batter's average
of 0.279. Measurement
has two inherent limitations, precision and accuracy. Precision is how reproducible a measurement
is from measurement to measurement.
Accuracy is how close to the actual measurement or truth a measurement
is. Accuracy is governed largely by
the quality of the instruments used for making the measurement. Precision can be limited by time and expense
in making multiple measurements.
However, the precision of a measurement can be determined
statistically by examining the variation or deviation in the measurements
from the average of the measurements. |
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Experimental
Error A
consideration in all measurement is that all measurements involve error. Thus it is important when making
measurements to consider sources of error so that we know what the
limitations of our measurements would be. There are three potential sources
of error in any measurement. These are
systematic, personal and random.
Systematic errors are determinate errors in that the error is made in
the same direction and typically with the same magnitude. A miscalibrated
thermometer would cause a systematic error.
Personal errors are introduced when the operator misreads a scale or
spills a solution. Random errors are
the small errors that occur each time a measurement is made and relate
specifically to the precision of the measurement. We can use statistical methods to assess
random errors and the measure that we use is called standard deviation. Standard deviation is a measure of the
spread of measurements from the mean or average and is is
discussed in Appendix A1.5 (pA10-A12) in your text. Many
scientific calculators and computer spreadsheets have this as a built in
function. So what does standard
deviation tell us? Basically it says
that the true mean has about a 67% chance of being within plus or minus one
standard deviation, a 95% chance of being within two and a 99% chance of
being within three standard deviations.
Thus, when we determine the standard deviation of a set of data we are
making an estimate of the precision of the data. |
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Graphs Another
important aspect to the analysis of data is preparing graphs. Graphs present a visual relationship
between two variables in an experiment.
Graphs should be titled with each axis labeled. The units should be indicated in
parentheses in the label. Graphs can
also show mathematical relationships.
Of particular interest in science (and other fields) is to show linear
relationships within data sets. Using
computer spreadsheet programs graphs can now be easily drawn and modified. |
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Materials Balance,
metric, at least 300 g capacity Plastic
Pipette Meter
stick, 100 cm Graduated
cylinder, 100 mL Thermometer,
centigrade & Fahrenheit Straw Pennies Beakers,
50 mL and 250 mL Ruler,
30 cm Procedure Mass
Measurement A. 1. Obtain two groups of ten pennies
each. One group should be minted
before 1981, the second should be from 1981 to the
present. 2. Weigh each penny in each group on the
balance. 3. Prepare a chart or table of your
data. Calculate the mean and standard
deviation for each group. 4. Using the above information determine
whether or not there is a significant difference in the mean. (See Appendix
in your textbook) Mass
Volume Measurement A. 1. Obtain a 100 mL
graduated cylinder. Determine the mass
of the cylinder empty. 2. Determine the mass of the cylinder with 15, 30, 45, 60 and
75 ml of water. 3. Plot a graph of mass (dependant
variable) versus water volume (independent variable). 4. Determine the relationship between
metric volume and mass (i.e. what is the slope). What is the intercept? What is the relationship between mL and cm3? What is the relationship between mL and grams? Mass-Volume
Measurement B 1. Measure
the length and diameter of a straw. Convert
volume to cm3 . 2. Determine
its volume from the formula for a cylinder.
Using a beaker of water and a pipette, obtain 10 straw volumes of
water and place them in a pre-weighed beaker.
3. Divide
the accumulated mass by ten (after subtracting the weight of the beaker)
Convert the mass to a volume using the relationship from above and compare
with your calculated volume. 4. What
is the purpose of using ten volumes instead of one? Linear Measurement B 1. Using the meter stick to measure the dimensions of
the classroom.. 2. Use your measurements to make a
scale drawing of the classroom. Use a scale of 2 cm = 1 m Temperature
Measurement 1. Using the Fahrenheit and centigrade
thermometers measure the temperature of water at five different centigrade
temperature about 10 degrees apart each. 2. Prepare a graph of your data. 3. Compute the formula for a line
through the data points of your graph.
How does the formula for the line compare with the conversion formulas
for centigrade to Fahrenheit? |
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Questions 1. Why do you think that we use mL rather than L to measure the volume of the beakers? 2. Where was the metric system developed
and when? 3. What two advantages of the metric
system over the English system of measurement? 4. In a paper get the batting averages
of the top ten Giants players and the top ten A's players with greater than
100 at bats. Average their batting
averages and compute the standard deviation.
Is there a significant difference between means of the averages of the
two teams? You can probably also get
this information on the Internet. 5. Name three commonly used items that
have metric rather than English measurements. |
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