Systems of Measurement
At the end of this chapter, the reader should be able to do the following:
1. State the units of measurement used in the United States Customary System.
2. State the units of measurement used in the metric system.
3. Convert units of measurement within the metric system.
4. Convert units of measurement between the metric system and the United States Customary System.
5. Compare and contrast the freezing and boiling points of water in the Celsius, Fahrenheit, and Kelvin temperature systems.
6. Convert among the Celsius, Fahrenheit, and Kelvin methods of temperature measurement.
MEASUREMENT OF LENGTH, WEIGHT, AND MASS
United States Customary System
Systems of weights and measures have been in existence since the first trade occurred among prehistoric peoples. The Egyptians used the cubit, which may be the earliest known use of linear measurement. One cubit was the distance between the elbow and the tip of the little finger. Later, the Greeks and Romans adopted many of the measurements used in the Egyptian system. The United States Customary System of measurement is based on the English system of measurement, which draws largely from the Greek and Roman systems. The United States is one of a handful of countries in the world that still use this system. Scientists and most other countries prefer the metric system. However, in the United States, efforts to persuade the American public to adopt the metric system have not succeeded. Americans want their foot-long hot dogs, their gallons of milk, and their miles of road. However, change may come from the business community as international trade agreements mandate the use of the metric system as the standard for measurements.
U.S. Customary System of Measurement of Length and Area
Measurement of length in this system begins with the inch and progresses to the mile and acre.
| 12 inches | = 1 foot |
| 3 feet (36 inches) | = 1 yard |
| 220 yards | = 1 furlong |
| 8 furlongs | = 1 mile |
| 1760 yards | = 1 mile |
| 5280 feet | = 1 mile |
| 1 square foot | = 144 square inches |
| 1 square yard | = 9 square feet |
| 43,560 square feet | = 1 acre |
| 1 square mile | = 640 acres |
U.S. Customary System of Liquid or Dry Measurement
Measurement of liquids begins with the teaspoon and progresses to the gallon.
| 1 teaspoon | = ⅓ tablespoon |
| 2 tablespoons | = 1 fluid ounce |
| 1 fluid ounce | =  cup |
| 2 fluid ounces | = ¼ cup |
| 2⅔ fluid ounces | = ⅓ cup |
| 4 fluid ounces | = ½ cup |
| 5⅓ fluid ounces | = ⅔ cup |
| 6 fluid ounces | = ¾ cup |
| 8 fluid ounces | = 1 cup |
| 2 cups | = 1 pint |
| 2 liquid pints | = 1 liquid quart |
| 4 liquid quarts | = 1 gallon |
Measurements of dry volumes include the following:
| 1 dry quart | = 2 dry pints |
| 8 dry pints | = 1 peck |
| 4 pecks | = 1 bushel |
Avoirdupois
| 1 dram | =  grains |
| 16 drams | = 1 ounce |
| 16 ounces | = 1 pound |
| 7000 grains | = 1 pound |
| 100 pounds | = 1 hundredweight |
| 2000 pounds | = 1 short ton |
| 2240 pounds | = 1 long ton |
As you can see, these measurements are not consistent with one another, which leads to confusion among systems. It was because of this inconsistency that another method of measurement that could be standardized was sought. That system is the metric system, which was developed in France in the 1790s.
Metric System
The metric system is based on fixed standards and on a uniform scale of 10. There are three basic units of measurement for length, weight, and volume. The basic units are as follows:
| length | = meter |
| mass | = gram |
| volume | = liter |
The meter is defined as the length of the path traveled by light in a vacuum in 
of a second. The kilogram, or 1000 g, is defined as the mass of water contained by a cube whose sides are one-tenth the length of a meter or one decimeter in length. The liter is defined as the volume of liquid contained within that same cube.
Another measurement is area. This is a derivation of the measurement of length. By multiplying the length times the width of a square surface, the area of the surface can be determined. Area is measured in squared units. Common laboratory metric area measurements are mm2, cm2, and m2.
Prefixes before the basic units of measurement inform the reader if a measurement is larger or smaller than the basic unit. Memorizing the prefixes and their abbreviations in Table 3–1 will be helpful in learning the metric system.
TABLE 3–1
Metric System Prefixes and Abbreviations
| Prefix | Abbreviation | Comparison to Basic Unit of 1 Gram, Meter, or Liter |
| Femto | f | 10-15 smaller |
| Pico | p | 10-12 smaller |
| Nano | n | 10-9 smaller |
| Micro | μ | 10-6 smaller |
| Milli | m | 10-3 smaller |
| Centi | c | 10-2 smaller |
| Deci | d | 10-1 smaller |
| Deca | Da | 101 larger |
| Hecto | H | 102 larger |
| Kilo | K | 103 larger |
| Mega | M | 106 larger |
Conversion Among Different Measurements Within the Metric System
Because the metric system is based on a scale of 10, conversion among different measurements within a unit is relatively simple (Table 3–2). A basic ratio and proportion calculation is all that is needed to perform the conversion.
TABLE 3–2
| Unit | Abbreviation | Comparable Unit |
| 1 megameter | (Mm) = | 1,000,000 or 106 meters |
| 1 kilometer | (Km) = | 1000 meters |
| 1 deciliter | (dL) = | 0.1 or 10-1 liters |
| 10 deciliters | (dL) = | 1 liter |
| 1 centimeter | (cm) = | 0.01 or 10-2 meters |
| 10 centimeters | (cm) = | 1 decimeter |
| 1 milliliter | (mL) = | 0.001 or 10-3 liters |
| 1 millimeter | (mm) = | 0.001 or 10-3 meters |
| 10 millimeters | (mm) = | 1 centimeter |
| 1 microgram | (μg) = | 0.000001 or 10-6 grams |
| 1000 micrograms | (μg)= | 1 milligram |
| 1 nanometer | (nm) = | 0.000000001 or 10-9 meters |
| 1000 nanometers | (nm) = | 1 micrometer |
| 1 picogram | (pg) = | 0.000000000001 or 10-12 grams |
| 1000 picograms | (pg) = | 1 nanogram |
| 1 femtoliter | (fL) = | 0.000000000000001 or 10-15 liters |
| 1000 femtoliters | (fL) = | 1 nanoliter |
| 1 cm2 | = | 100 mm2 |
| 1 m2 | = | 1,000,000 mm2 |
| 1 mm3 | = | 1 microliter |
| 1 cm3 | = | 1 milliliter |
In the clinical laboratory, many analytes—such as glucose—are measured in terms of milligrams per deciliter or the number of milligrams contained in 1 dL of plasma. Other analytes, such as the hormone prolactin, are measured in terms of nanograms per milliliter. In hematology, white blood cells historically are counted in terms of cubic millimeters (mm3)or currently expressed in units of liters of whole blood. The mean corpuscular volume (MCV) is measured in femtoliters.
In other areas of healthcare, the metric term micro (0.000001 or 10−6) tends to be abbreviated as mc, but in the clinical laboratory as the Greek symbol μ. For example, microgram is frequently abbreviated as mcg for drug dosages, but as μg in the clinical laboratory.
Example 3–1
How many milliliters are in a 2.0-L soda bottle?
In order to convert liters to milliliters, the basic value of each must be known. According to Table 3–2, 1 mL is 10-3 smaller than the base value of 1 L; therefore, there are 1000 mL in 1 L.
As discussed in more detail in Chapter 4, ratio and proportion is a great math tool that can be used for many laboratory calculations provided that there is a proportional relationship between two ratios. A ratio can be expressed as a fraction with a numerator (the top number of the fraction) and a denominator (the lower or bottom number of the fraction). In the following example, both the numerators are liters and the denominators are in milliliters. The relationship ratio is that there are 1000 mL in 1 L, which can be also expressed in scientific notation as 103 mL are equal to 1 L. Therefore, X mL = 2 liters is also a proportional relationship. To solve a ratio and proportion calculation, the numerator of the first ratio (1 L) is multiplied by the denominator of the second ratio (X mL). The denominator of the first ratio (1000 mL) is then multiplied by the numerator of the second ratio (2 L). This is called crossmultiplication. The liter units will cancel out leaving the final result in milliliters.
Crossmultiplying the equation derives:
There are 2000 mL (2.0×103 mL) in a 2.0-L soda bottle.
How many deciliters are in 3.5 L?
Crossmultiplying the equation and solving for X:
Using ratio and proportion, the answer is 35 dL or 3.5 × 101 dL.
How many milligrams are in 1.0 g?
From Table 3-1, a milligram is 10-3 smaller than a gram. Using ratio and proportion:
Therefore, the answer is 1000 mg or 1.0 × 103 mg.
How many centimeters are in 1 km?
This problem can be solved in two stages. First, using ratio and proportion or the chart, convert kilometers into meters. There are 1000 m in 1 km. Next, convert the 1000 m into centimeters. Since there are 100 cm in 1 m, then by using ratio and proportion, the final answer is 100,000 cm or 1.0 × 105 cm.
String method
A shortcut way to perform conversions is called the “string” method. In this method, the number that you want to convert into a different unit is multiplied by an equivalent ratio or ratios. The units will cancel out and you will end up with the desired result. A benefit of this method is that although you need to know the relationships between the basic unit and the prefix units, you don’t need to know exact equivalents such as how many picograms are in a microgram. Using the string method to solve the first example problem yields the following equation:
The last example problem can be solved by:
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