1.8.6 Assessment

As we get further into problem solving, you will need to decide whether or not the answer to a problem “makes sense.” To determine this, at least until you have more experience with SI units, you may need to convert from SI units back to the English units in which you think. But this conversion does not need to be very accurate. For example, if you are working a problem about automobile speeds and reach an answer of $35 m / s$ , all you really want to know is whether or not this is a realistic speed for a car. That requires a “quick and dirty” conversion, not a conversion of great accuracy.

TABLE 1.5 shows several approximate conversion factors that can be used to assess the answer to a problem. Using $1 m / s \approx 2 mph$ , you find that $35 m / s$ is roughly 70 mph, a reasonable speed for a car. But an answer of $350 m / s$ , which you might get after making a calculation error, would be an unreasonable 700 mph. Practice with these will allow you to develop intuition for metric units.

TABLE 1.5 Approximate conversion factors. Use these for assessment, not in problem solving.

1 cm \approx \frac{1}{2} i n

10 cm \approx 4 i n

1 m \approx 1 y a r d

1 m \approx 3 f e e t

1 km \approx 0.6 m i l e

1 m / s \approx 2 m p h

NOTE These approximate conversion factors are accurate to only one significant figure. This is sufficient to assess the answer to a problem, but do not use the conversion factors from Table 1.5 for converting English units to SI units at the start of a problem. Use Table 1.4.