Section 4.9 Changing Magnitude of the Dimension

As shown in Figure 4.7.1, SI units have prefixes that are based on a power of 10 to change the magnitude of the dimension. USCS units, however, are not as simple to change from one magnitude to another and require a unit change such as feet to inches or feet to miles. Some of these unit changes are provided below:

\(1\,foot=12\,inches\)

\(1\,mile=5280\,feet\)

\(1\,ton=2000\,lb\)

\(1\,kip=1000\,lb\)

It is important to note that both ft and in are units for dimensions of length which is why you can convert between them. The same goes for the units ton, lb, and kip as these are all units for the dimension of force.

Let’s do an example of unit conversion between feet and inches. My nephew is 77 inches tall. I think for most of us we wouldn’t be able to intuitively know if that was tall of short without converting to feet for a better understanding. So let’s do that:

\(77\,in*\frac{1\,ft}{12\,in}=\frac{77}{12\,ft}=6.42\,ft\)

6.42 ft sounds pretty tall! We are used to seeing height in units of both ft and inches so now let’s try to turn that .42 into inches:

\(0.42\,ft* \frac{12\,in}{1\,ft}=5\,in\)

We also use unit conversions to switch between unit systems. Let’s talk more about unit conversions in the next chapter.