1 INTRODUCTION 1.6 Precision and significant figures(^)
1 cm = 10 −^2 m
1 g = 10 −^3 kg
1 ft = 0.3048 m
1 lb = 4.448 N
1 slug = 14.59 kg
Table 2: Conversion factors
1.6 Precision and significant figures
In this book, you are expected to perform calculations to a relative accuracy of
1%: i.e., to three significant figures. Since rounding errors tend to accumulate
during lengthy calculations, the easiest way in which to achieve this accuracy is to
perform all intermediate calculations to four significant figures, and then to round
the final result down to three significant figures. If one of the quantities in your
calculation turns out to the the small difference between two much larger num-
bers, then you may need to keep more than four significant figures. Incidentally,
you are strongly urged to use scientific notation in all of your calculations: the
use of non-scientific notation is generally a major source of error in this course.
If your calculators are capable of operating in a mode in which all numbers (not
just very small or very large numbers) are displayed in scientific form then you
are advised to perform your calculations in this mode.
1.7 Dimensional analysis
As we have already mentioned, length, mass, and time are three fundamentally
different quantities which are measured in three completely independent units. It,
therefore, makes no sense for a prospective law of physics to express an equality
between (say) a length and a mass. In other words, the example law
m = l, (1.3)
where m is a mass and l is a length, cannot possibly be correct. One easy way of
seeing that Eq. (1.3) is invalid (as a law of physics), is to note that this equation is
dependent on the adopted system of units: i.e., if m = l in mks units, then m /= l