1 Skills, Methods, and the Nature of Physics - BC Science Physics 11

Accuracy and
Precision
In another example, the volume of a liquid is said to be 600 mL. How precise is this
measurement? Did the measurer mean it was “around 600 mL”? Or was it 600 mL to the
nearest millilitre? Perhaps the volume was measured to the nearest tenth of a millilitre.
Only the measurer really knows. Writing the volume as 600 mL is somewhat ambiguous.
To be unambiguous, such a measurement might be expressed in scientific notation.
To do this, the measurement is converted to the product of a number containing the
intended number of significant digits (using one digit to the left of the decimal point)
and a power of 10. For example, if you write 6 × 10 2 mL, you are estimating to the nearest
100 mL. If you write 6.0 × 10 2 mL, you are estimating to the nearest 10 mL.
A measurement to the nearest millilitre would be 6.00 × 10 2 mL. The zeros here are
measured zeros, not just decimal-placing zeros. They are significant digits.
If it is not convenient to use scientific notation, you must indicate in some other
way that a zero is a measured zero. For example, if the volume of a liquid is measured to
the nearest mL to be “600.” mL, the decimal point will tell the reader that you measured
to the nearest mL, and that both zeros are measured zeros. “600. mL” means the same as
6.00 × 10 2 mL.
The number of significant digits used to express the result of a measurement
indicates how precise the measurement was. A person’s height measurement of 1.895 m
is more precise than a measurement of 1.9 m.
Measured values are determined using a variety of different measuring devices. There are
devices designed to measure all sorts of different quantities. The collection pictured in
Figure 1.3.1 measures temperature, length, and volume. In addition, there are a variety of
precisions (exactnesses) associated with different devices. The micrometer (also called a
caliper) is more precise than the ruler while the burette and pipette are more precise than
the graduated cylinder.
Figure 1.3.1 A selection of measuring devices with different
levels of precision
Despite the fact that some measuring devices are more precise than others, it is
impossible to design a measuring device that gives perfectly exact measurements. All
measuring devices have some degree of uncertainty associated with them.
The 1-kg mass shown in Figure 1.3.2 is kept in a helium-filled bell jar at the BIPM
in Sèvres France. It is the only exact mass on the planet. All other masses are measured
relative to this and therefore have some degree of uncertainty associated with them.
10 Chapter 1 Skills, Methods, and the Nature of Physics © Edvantage Interactive 2012 ISBN 978-0-9864778-3-6