Consider the measurement of a football field a third time. Measured accurately roughly, to the nearest
foot using a metre stick marked at tenths of a metre the most likely measured value will be 91.4 m. This
value has three significant digits. Thus, the accuracy of a measurement and not the units employed determines
the number of significant figures in a measured amount.* This last example illustrates the situation
of converting an analysis in feet to expression in metres.
In the case of a football field measurement, it is easy to identify the significant digits. This is not always
the case. Consider the value 4 in. It may be known that there is one significant digit. But, in some cases, the
intended quantity maybe 4.0,4.00, or 4.000 0, etc. The latter of these, 4.000 0 in., implies 4 in. Measured to
the nearest ten-thousandth of an inch. Accuracy must be specified in some manner either as to the accuracy or as
several significant digits.
The measurement of a football field to the nearest foot implies an accuracy of ± 0.5 ft. What this means
is that as a result of the measurement it is known that the length of the field is 100 ft ± 0.5 ft which means
that the field length is between 299.5 ft and 300.5 ft. The accuracy of this measurement can also be
expressed as a percentage: ± (0.5 ft/300, ft) X 100% or ± 0.167%. In the case of the measured value 4.0000
in., having five significant digits, the implied accuracy is ± 0.000 05 in. This can be expressed as ± (0.000 05
in./4.0000 in.) 100% which equals ± 0.00125%.
Note that zeros may be either significant digits or they may only indicate the magnitude of a number. In
the date, 1970, the zero is a significant digit. The population of the U.S. in 1960 rounded to the nearest
thousand, 179 323 000, the zeros indicate magnitude but are not significant digits. The zeros in 0.001 32 are
not significant digits.
Finally, consider exact counts of objects, such as four trucks, $38.25, and 31 transistors. These numbers can
be treated as though they have an infinite number of significant digits at https://scientificnotationconverter.info/