Measurement
Precision
Unless there is a digital display, always measure
to one spot beyond the smallest unit of CERTAIN measurement of
the tool. For example, if you use a ruler that can accurately
measure to the tenth of a centimeter, your measurement would be
to the hundredth of a centimeter. The number of
significant digits should reflect the precision of
the measurement. There should be no variation in the
precision of raw data. In other words, the same number of digits
past the decimal place should be used. For data derived
from processing raw data (i.e., means), the level
of precision should be consistent with that of
the raw data.
You may need to
estimate the degree of precision sometimes especially with stop watches.
Digital stop watches are said to be accurate to 0.01s but human reaction
time is only ±0.1s.
For electronic probes you may have to go to the manufacturer's specifications
(on their web site or in the instructions manual).
Uncertainty
All measurements have uncertainties and are only as
accurate as the tool being used to make the measurement. For general purposes, the accuracy of
a measurement device is one half of the smallest measurement possible with the device.
To determine uncertainty:
- Find the smallest increment of
measurement on your measurement device
- Divide it by two
- Round to the first non-zero
number
So, for example, the rulers in class measure to the millimeter
(0.10 cm). Therefore, the ruler’s
measurement uncertainty is +/- 0.05 cm.
The numerical value of a ± uncertainty value tells you the range of the result.
For example a result reported as 1.23 ± 0.05 means that the experimenter has
some degree of confidence that the true value falls in between 1.18 and 1.28.
Examples:
- Mass of a
penny on a centigram balance:
3.12g (± 0.05g)
- Temperature using
a typical lab thermometer: 25.5°C (± 0.5°C)
Experimental uncertainties should be rounded UP to one significant
figure. Uncertainties are almost always quoted to one significant
digit and we round up because it’s better to suggest higher uncertainty than to
imply there is less uncertainty.
- Wrong: ± 12.5 mL
- Correct: ± 20 mL
The measurement should have the same number of digits (decimal places) as the
uncertainty. It would be confusing to suggest
that you knew the digit in the hundredths (or thousandths) place when you
admit that you unsure of the tenths place.
- Wrong: 1.237 s ±
0.1 s
- Correct: 1.2 s ± 0.1 s
Just as for units, in a column of data students can
show the uncertainty in the column heading and don’t have
to keep rewriting if for every measurement in the table.
Units
A measurement without units is meaningless! The system
of units used in science is called the International System of
Units (SI units). In the table below are some of the
more common SI units used. When measuring time, it is
acceptable to use minutes, days or hours when the experiment
spans over a significant period of time. When showing length, it is acceptable
to use the associated units shown in the table below.
The following
example shows different ways to express the same unit.
- Oxygen
consumption (milliliters per gram per hour)
- Oxygen consumption (ml/g/h)
- Oxygen
consumption (ml g-1 h-1)