1.8.5 Unit Conversions

Although SI units are our standard, we cannot entirely forget that the United States still uses English units. Thus it remains important to be able to convert back and forth between SI units and English units. TABLE 1.4 shows several frequently used conversions, and these are worth memorizing if you do not already know them. While the English system was originally based on the length of the king’s foot, it is interesting to note that today the conversion $1 in = 2.54 cm$ is the definition of the inch. In other words, the English system for lengths is now based on the meter!

TABLE 1.4 Useful unit conversions

1 in = 2.54 c m

1 mi = 1.609 k m

1 mph = 0.447 m / s

1 m = 39.37 i n

1 km = 0.621 m i

1 m / s = 2.24 m p h

There are various techniques for doing unit conversions. One effective method is to write the conversion factor as a ratio equal to one. For example, using information in Tables 1.3 and 1.4, we have

\frac{10^{- 6} m}{1 μ m} = 1 and \frac{2.54 cm}{1 in} = 1

Because multiplying any expression by 1 does not change its value, these ratios are easily used for conversions. To convert $3.5 μ m$ to meters we compute

3.5 μ m \times \frac{10^{- 6} m}{1 μ m} = 3.5 \times 10^{- 6} m

Similarly, the conversion of 2 feet to meters is

2.00 ft \times \frac{12 in}{1 ft} \times \frac{2.54 cm}{1 in} \times \frac{10^{- 2} m}{1 cm} = 0.610 m

Notice how units in the numerator and in the denominator cancel until only the desired units remain at the end. You can continue this process of multiplying by 1 as many times as necessary to complete all the conversions.

A photo of the Mars Climate Orbiter in the Martian atmosphere. — In 1999, the $125-million Mars Climate Orbiter burned up in the Martian atmosphere instead of entering a safe orbit. The problem was faulty units! The engineering team supplied data in English units, but the navigation team assumed that the data were in metric units.