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1.4: The Metric System

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    25017
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    In order to make consistent measurements of physical phenomena, some system of measurement needs to be standardized. While almost any scheme can be made to work, some systems are more logical and easier to deal with than others. The current standard in the world of science and technology is the metric system, or more properly, the International System of Units (abbreviated SI, from the French Système International). This standard has found wide adoption across the globe and is the system used by roughly 95% of the human population. This is in contrast to the system of USA customary units which is based on a prior system of units originating in England. It should be noted that the USA, comprising some 5% of the global population, is the only country of reasonable economic power left that has not adopted the metric system for general use. This is only true in the consumer realm though as virtually all scientists, engineers and technicians in the USA routinely use the metric system1. Even many products built and sold in the USA use metric components internally; it's just not noticed by the consumer.

    Why has the metric system seen such wide adoption compared to USA customary units? The simple answer is because it is an easier system to learn and manipulate. First, a main strength of the metric system is that everything is based on powers of ten. Second, customary units often consist of many different variations on a single parameter while the metric system uses just a single parameter. For example, consider the measurement of length. For human-size lengths we might measure something in inches or feet. If it's a bit larger we might use yards. If it's even farther, we would use miles. In the metric system there is just one unit for length and that's the meter (roughly 39.37 inches). If we want to talk about particularly small or large values we would simply add our engineering notation prefixes to come up with millimeters or kilometers for everyday conversion (although if a value happened to be particularly large or small we would say something like 2.3E9 meters).

    But customary units complicate the system even more because the various versions of a parameter are usually not based on a power of ten. For example, there are 12 inches in a foot and 5280 feet in a mile. This is further complicated by the fact that there is more than one kind of mile (the common statute mile is 5280 feet but the nautical mile is roughly 6076 feet). Similarly, if we measure the weight of something we could use ounces, pounds and tons (more than one kind), and again, the conversion factors are not convenient (16 ounces to the pound, 2000 pounds to the common ton).

    These odd conversion factors unnecessarily complicate matters. For example, suppose we have a length measurement of 2 feet, 8 1/2 inches and we need to multiply this by a factor of 3. Multiplying each part by three yields 6 feet, 25 1/2 inches, but that needs to be simplified to 8 feet, 1 1/2 inches. This extra step can be avoided if we base everything on powers of ten.

    For individuals only familiar with USA customary units, the ease of the metric system can be illustrated with currency. USA currency is, in effect, metric: 100 cents make up one dollar. Simply imagine how difficult it would be if, instead of cents, a dollar consisted of 13 flarkneks and 85 dollars made up a skroon. Further, imagine you decide to buy a new computer that costs 21 skroon, 10 dollars and 12 flarkneks. Now compute the total with a 6.5% local tax rate. Will 22 skroon be enough? What's the change? Ouch! It's not impossible but it's extra error prone work. That's precisely the issue with feet, miles, ounces, pounds, pints, gallons and so on.

    In the metric system typically we use the MKS variation: \(m\)eters for length or distance, \(k\)ilograms for mass and \(s\)econds for time. Further, we typically use liters for volume (liquid measure) and Celsius (AKA Centigrade) for temperature, although it is sometimes more convenient to use the absolute temperature scale of kelvin. Fortunately, the thermal energy indicated by a one degree Celsius change is identical to that for kelvin. The two schemes only differ in their zero reference point (absolute zero for kelvin and the point at which water freezes for Celsius).

    As virtually all of the calculations presented in this text are metric, there is little need to concern ourselves with conversions back and forth between the two systems. Indeed, if the USA were to finally make the switch to metric, no one would ever need to concern themselves with conversions, with the possible exception of historians, and perhaps people trying to recreate old family recipes and the like.

    Sometimes, careless people tend to think of units of measure as an afterthought. Don't get caught in this trap. Failure to pay attention to proper units can have catastrophic results. One example is the Mars Climate Orbiter. In 1999 this mission to study the planet Mars suffered a spectacular failure. A subcontractor had used USA customary units for its software which then fed values to other systems that were expecting metric/SI units (as specified in the system contract). The result was the destruction of the orbiter as it attempted orbital insertion. The cost of the mission was nearly $330 million, completely wasted.

    A table of commonly used quantities, their SI units and typical equivalents is shown in Table 1.4.1 . Further details on units can be found in Appendix E.

    Quantity (abbreviation) Unit (abbreviation) Approximate Equivalent
    Length (l) meter (m) 1 m \(\approx\) 39.37 inches
    Mass (\(m\)) kilogram (kg) 1 kg \(\approx\) 2.2 pounds (on Earth)
    Time (t) second (s) NA
    Force (\(F\)) newton (N) 1 N \(\approx\) 0.225 pound-force
    Energy (\(w\)) joule (J) 3.6E6 J \(\approx\) 1 kWh
    Power (P) watt (W) 746 W \(\approx\) 1 horsepower
    Temperature (T) kelvin (K) or Celsius (\(^{\circ}\)C) Fahrenheit = \(32 + 9/5 \cdot ^{\circ}\)C kelvin = \(^{\circ}\)C + 273.15
    Electric Charge (Q) coulomb (C) NA
    Current (I) amp (A) NA
    Voltage (V or E) volt (V) NA
    Table 1.4.1 : Common quantities, SI units and equivalents. Note: As a general rule, when units are abbreviated they are capitalized. When they are spelled out they are treated as common nouns and therefore not capitalized, even when named in honor of someone (an exception being some temperature scales).

    References

    1It is also true of consumers who buy soda and similar beverages that are routinely sold in metric two or three liter bottles. Go figure.


    This page titled 1.4: The Metric System is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by James M. Fiore via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.