**Introduction to Unit Conversions**

With all the different systems of units in use throughout the world, the business of conversion from one system to another has become the subject matter for whole books. Web sites are devoted to this task; at the time of this writing, a good site could be found at Test and Measurement World ( *www.tmworld.com* ). Click on the “Software” link, and then go to the page called “Calculator Programs.”

**A Simple Table**

Table 6-3 shows conversions for quantities in base SI units to other common schemes. In this table and in any expression of quantity in any units, the coefficient is the number by which the power of 10 is multiplied.

**Table 6-3** Conversions for Base Units in the International System (SI) to Units in Other Systems (When no coefficient is given, it is exactly equal to 1.)

This is by no means a complete table. It is amazing how many different units exist; for example, you might someday want to know how many bushels there are in a cubic kilometer! Some units seem to have been devised out of whimsy, as if the inventors knew the confusion and consternation their later use would cause.

**Dimensions**

When converting from one unit system to another, always be sure you’re talking about the same quantity or phenomenon. For example, you cannot convert meters squared to centimeters cubed or candela to meters per second. You must keep in mind what you’re trying to express and be sure that you are not, in effect, trying to change an apple into an orange.

The particular thing that a unit quantifies is called the *dimension* of the quantity or phenomenon. Thus meters per second, feet per hour, and furlongs per fortnight represent expressions of the speed dimension; seconds, minutes, hours, and days are expressions of the time dimension. Units are always associated with dimensions. So are most constants, although there are a few constants that stand by themselves (π and *e* are two well-known examples).

**Units of Conversions Practice Problems **

**Problem 1**

You step on a scale, and it tells you that you mass 63 kilograms. How many pounds does this represent?

**Solution 1**

Assume that you are on the planet Earth, so your mass-to-weight conversion can be defined in a meaningful way. (Remember, mass is not the same thing as weight.) Use Table 6-3 . Multiply 63 by 2.205 to get 139 pounds. Because you are given your mass to only two significant figures, you must round this off to 140 pounds to be purely scientific.

**Problem 2**

You are driving in Europe and you see that the posted speed limit is 90 kilometers per hour (km/h). How many miles per hour (mi/h) is this?

**Solution 2**

In this case, you only need to worry about miles versus kilometers; the “per hour” part doesn’t change. Thus you convert kilometers to miles. First remember that 1 km = 1,000 m; then 90 km = 90,000 m = 9.0 × 10 ^{4} m. The conversion of meters to statute miles (these are the miles used on land) requires that you multiply by 6.214 × 10 ^{−4} . Therefore, you multiply 9.0 × 10 ^{4} by 6.214 × 10 ^{−4} to get 55.926. This must be rounded off to 56, or two significant figures, because the posted speed limit quantity, 90, only goes that far.

**Problem 3**

How many feet per second is the speed limit in Problem 2?

**Solution 3**

This is a two-step problem. You’re given the speed in kilometers per hour. You must convert kilometers to feet, and you also must convert hours to seconds. These two steps should be done separately. It does not matter in which order you do them, but you must do both conversions independently if you want to avoid getting confused. (Some of the Web-based calculator programs will do it all for you in a flash, but here, all we have is Table 6-3 .)

Let’s convert kilometers per hour to kilometers per second first. This requires division by 3,600, the number of seconds in an hour. Thus 90 km/h = 90/3600 km/s = 0.025 km/s. Now convert kilometers to meters; multiply by 1,000 to obtain 25 m/s as the posted speed limit. Finally, convert meters to feet; multiply 25 by 3.281 to get 82.025. This must be rounded off to 82 ft/s, again because the posted speed limit is expressed to only two significant figures.

Practice problems of these concepts can be found at: Units And Constants Practice Test

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