Systems of 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

U.S. Systems for Measurement of Mass

At present, there are four different measurement systems used in the United States to measure weight.

1. Troy: used to weigh silver, gold, and other precious metals

2. Apothecaries: used by pharmacists to weigh drugs

3. Avoirdupois: used for general purposes

4. Metric system: used in science

Troy

1 pennyweight	= 24 grains
20 pennyweights	= 1 ounce
12 ounces	= 1 pound
5760 grains	= 1 pound
3.2 grains	= 1 carat

Apothecaries

1 scruple	= 20 grains
3 scruples	= 1 dram
8 drams	= 1 ounce
12 ounces	= 1 pound
5760 grains	= 1 pound

Avoirdupois

1 dram	= 271132 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 1299,792,458 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

Common Metric System Units

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.