Measurements are comparisons between an unknown and a standard result. Accurate measurements are essential in chemistry. Today we drove right into common SI prefixes, and we explored the ideas of accuracy, and error. We were also introduced to some mind-boggling concepts, and had a laugh at a comical snippet of "The Big Bang Theory". The 7 fundamental units are mass (kg), distance (m), time (s), temperature (K), amount of substance (mol), current (A), and luminosity (cd).
SI PREFIXES
An SI prefix is a name that precedes a basic unit of measure. It indicates the multiple of the unit. Here are some common SI prefixes (next to each prefix is its multiplier):
femto (f) - 10-15
pico (p) - 10-12
nano (n) - 10-9
micro (μ) - 10-6
milli (m)- 10-3
centi (c) - 10-2
deci (d)- 10-1
deka (da)- 101
hecto (h)- 102
kilo (k) - 103
mega (M) - 106
giga (G)- 109
tera (T)- 1012
peta (P)- 1015
Prefixes are used in many areas of our daily lives. Here are a few examples of places that you may see prefixes being used:
Atoms: picometers
Viruses: nanometers
Cells: micrometers
Computers: kilobytes, megabytes, gigabytes, terabytes
SD cards: gigabytes
Cameras: megapixels
Automobiles: kilometres per hour
ACCURACY VS. PRECISION
Accuracy is the degree of closeness of a measured or calculated quantity to its actual (true) value. In other words, it means getting a result that is close to the real answer. Precision is the degree to which further measurements or calculations show the same or similar results. That is, getting a similar result every time you try. A good analogy is that of a dartboard:
EXPRESSING ERROR
In chemistry, the definition of an error is a discrepancy between a computed, observed, or measured value or condition and the true, specified, or theoretically correct value or condition. It is a fundamental part of science and we learned that there are usually three reasons for error:
1. Physical errors in the measuring device
2. "Sloppy" measuring
3. Changing ambient conditions
Measurements are uncertain because they are never free of flaws, and estimation is always involved (whether using a digital display or scale). Because the last digit of the measurement is estimated, a plus-or-minus symbol, ±, is used to show the uncertainty of a measurement. To make your measurements as reliable as possible, read the scales and digital displays of your instruments carefully. Also, keep the instruments clean and ensure that they are in tip-top shape. Error is taken to be half the smallest division on your measuring device. There are two possibilities of error; absolute error and percent error.
Examples:
*Daniel measures the volume of a chemical to be 40.0mL. The actual value is 41.2mL. Determine the absolute error in this measurement.
absolute error = measured - accepted
absolute error = (40.0) - (41.2)
absolute error = -1.2
(Therefore, Daniel's measurement was off by 1.2mL. Because it is negative, his measurement was below the actual value.)
*Determine the percent error in this measurement.
percent error = [(absolute error) / (accepted value)] X 100
percent error = [(-1.2)/(41.2)] X 100
percent error = [-0.029126213] X 100
percent error = -2.912621359%
percent error = -2.9% (to 2 significant digits)
(Therefore, the percent error of the measurement was -2.9%. Because it is negative, his measurement was below the actual value.)
A meniscus is the curved upper surface of a still liquid in a tube, concave if the liquid wets the walls of the container, convex if it does not, caused by surface tension. With liquids such as water, the bottom of the curved surface of the liquid is the point where the reading is taken.
Here is a mind-boggling video of a hypercube - a figure in four or more dimensions with sides that are all of the same length and angles that are all right angles:
Next class, unit analysis!
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