0.4 1.5 physical quantities and units  (Page 3/17)

Metric prefixes

SI units are part of the metric system    . The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10. [link] gives metric prefixes and symbols used to denote various factors of 10.

Metric systems have the advantage that conversions of units involve only powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on. In nonmetric systems, such as the system of U.S. customary units, the relationships are not as simple—there are 12 inches in a foot, 5280 feet in a mile, and so on. Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by using an appropriate metric prefix. For example, distances in meters are suitable in construction, while distances in kilometers are appropriate for air travel, and the tiny measure of nanometers are convenient in optical design. With the metric system there is no need to invent new units for particular applications.

The term order of magnitude    refers to the scale of a value expressed in the metric system. Each power of $\text{10}$ in the metric system represents a different order of magnitude. For example, ${\text{10}}^1,{\text{10}}^2,{\text{10}}^3$ , and so forth are all different orders of magnitude. All quantities that can be expressed as a product of a specific power of $\text{10}$ are said to be of the same order of magnitude. For example, the number $\text{800}$ can be written as $8\times {\text{10}}^2$ , and the number $\text{450}$ can be written as $4.5\times {\text{10}}^2.$ Thus, the numbers $\text{800}$ and $\text{450}$ are of the same order of magnitude: ${\text{10}}^2.$ Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of ${\text{10}}^{-9}\text{ m,}$ while the diameter of the Sun is on the order of ${\text{10}}^9\text{ m.}$

Unit conversion and dimensional analysis

It is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook, some quantities may be expressed in units of liters and you need to convert them to cups. Or, perhaps you are reading walking directions from one location to another and you are interested in how many miles you will be walking. In this case, you will need to convert units of feet to miles.