The Metric System

Three base units are commonly used for metric measurement of medications to indicate weight, volume, and length.

An advanced form of ratios and proportions that cancels unwanted units in the conversion to establish the desired unit of measurement.

Equivalent

Equal in value.

The abbreviation for intramuscular.

The abbreviation for intravenous.

Metric System

Standardized international system of units and measurements based on powers of 10, also known as the International System of Units; used for most medication doses in the United States.

Milliequivalent

Another way to describe contents of medication in a solution.

Multidose Vial

A container that holds multiple doses of a specific medication in liquid format; the label reads mg/ml.

The abbreviation for medication given by mouth.

Prefix

Found at the beginning of a word to adjust or qualify its meaning.

Prescription

Orders written by a physician that outline the medication dose, frequency, and length of time for treatment.

Units

Units in the metric system refer to a dimension, such as weight (or mass), volume, and length.

Word Root

Place of origin; base unit.

Objective 1

Many of us have been exposed to the metric system since grade school. Through the years, knowledge of the metric system has become necessary in the fields of engineering, steel production, the automotive industry, and health care. The health care industry in the United States uses a combination of the metric system, household measurements, and the apothecary system in dispensing medications and educating patients about their medications. In this chapter, we focus on the metric system and common metric conversions.

MATH TRIVIA 7-1

The metric system was established in France in the early 1800s.

Objective 2

Prefixes and base units (word roots)

The metric system uses three base units (orword roots) to describe length, volume, and weight or mass. The three base units are as follows:

Meter (M, m) is used to describe length.

Liter (L) is used to describe volume. (The abbreviation for liter is always capitalized to avoid misinterpretation as the number 1.)

Gram (G, gm) is used to describe mass.

The base word can be manipulated by changing the prefix to describe larger and smaller measurements. Prefixes are found before the base word, as described in the following examples:

Kilometer	Kilo- is the prefix	Meter is the base word
Milliliter	Milli- is the prefix	Liter is the base word
Microgram	Micro- is the prefix	Gram is the base word

The following is a list of the prefixes used in the metric system and their meanings:

Micro- (mc)—millionth

Milli- (m)—thousandth

It is important to memorize these terms and the amounts they represent. A common mnemonic used to remember the prefix order from largest measurement to smallest is: Kangaroo Hop Down Mountains Drinking Chocolate Milk (Figure 7-1).

Figure 7-1 Mnemonic for remembering prefix order: Kangaroo Hop Down Mountains Drinking Chocolate Milk.

Human Error 7-1

Until recently, the symbol μg was used as the abbreviation for micrograms. The symbol was based on the Greek letter mu (μ). This symbol has been discontinued in the pharmacy fields because of the confusion between μg and mg in handwritten documents.

Miscommunication is a problem in the everyday world. Whether through the written or the spoken word, miscommunication results in many errors. People’s lives are in jeopardy when miscommunication occurs in the health care field. For this reason, measurements are documented in a manner that reduces the chance of miscommunication. If you have not been in the practice of labeling your answers, it is time to start. In health care, a number by itself means nothing; it must always be followed by an abbreviated label to avoid confusion.

Example:

A patient drank 250 ml at breakfast, 500 ml at lunch, and 525 ml at dinner. How much did the patient drink during his meals on this day? The correct answer is 1275 ml.

STRATEGY 7-1: Documentation

1. A number is always accompanied by an abbreviation.

Incorrect: 10

Correct: 10 L

2. Metric abbreviations are always singular. Adding the “s” will change the meaning of the abbreviation.

Incorrect: mls

Correct: ml

3. Periods are not used after metric abbreviations unless the abbreviation falls at the end of a sentence.

Incorrect: 50 ml. of fluid

Correct: 50 ml of fluid

4. If the amount is less than a whole number and is written as a decimal, a 0 is always placed before the decimal point.

Incorrect: .03

Correct: 0.03

MATH ETIQUETTE 7-1

The correct order to write metric units is as follows: 4 mg.

1. Write the amount: 4

2. Allow for a space between the amount and measurement.

3. Write the abbreviation for the prefix: m

4. Write the abbreviation for the word root: g

PRACTICE THE SKILL 7-1

Write the correct prefix or word root described by each question.

1. What is the metric measurement for volume? _________________

2. What is the prefix that means 11000? _________________

3. What is the metric measurement for length? _________________

4. What is the prefix that means 10? _________________

5. What is the metric measurement for weight or mass? _________________

6. What is the prefix that means 110? _________________

7. What is the prefix that means 1,000? _________________

8. What is the prefix that means 110,000,000? _________________

9. What is the prefix that means 1100? _________________

10. What is the prefix that means 100? _________________

Objectives 3, 4, 5

Conversion of measurements in the metric system

There are many ways to convert measurements in the metric system in order to determine equivalent measurements. In this chapter, we use the proportion and cross multiplication strategies learned in Chapter 5 and dimensional analysis. Let’s take a quick moment to review the steps for writing a proportion.

1. Read the problem.

2. Identify the known information.

3. Write your proportion so that the same units appear in the same location for each proportion.

4. Solve the problem using cross multiplication if your proportion is written as a fraction. If the problem is written in linear fashion, multiply the means (“inside” numbers) together and the extremes (“outside” numbers) together.

When you are working with equivalents, it is important to use the proper equivalent for the problem to be solved. If the improper equivalent is used, your answer will be off. Because of the use of equipment that allows precise measurements, rounding is not a common practice in health care.

STRATEGY 7-2: Solving Equivalency Problems

1. Establish what information is known.

2. Determine what is the known equivalent or conversion for which the problem is asking.

3. Write down what is known on the left side of the equation.

4. Write down the remaining known information on the right side of the equation.

5. Identify the unknown information with an “X” in the equation.

6. If possible, reduce fractions before cross multiplication.

7. Cross multiply and solve for the unknown as discussed in Chapter 5.

Example:
How many meters are in 3,000 mm?
1. Establish what information is known. The question is asking us to change millimeters to meters. 2. Determine what is the known equivalent or conversion for which the problem is asking. The known equivalent is 1,000 mm, which is the same as or equal to 1 meter. 3. Write down what is known on the left side of the equation. 1000mm1meter= 4. Write down the remaining known information on the right side of the equation. 1000mm1meter=3000mm 5. Identify the unknown information with an “X” in the equation. 1000mm1meter=3000mmX 6. If possible, reduce fractions before cross multiplication. 1000mm1meter=3000mmX 7. Cross multiply and solve for the unknown as learned in Chapter 5. 1000mm1meter=3000mmX 1000X1000=30001000 X = 3 Answer: 3 meters
Check your answer by substituting 3 for “X” and solving the problem.

Further examples:
1. How many cm are in 2.5 meters? 100cm1M=Xcm2.5M or 100 cm : 1 M :: X cm : 2.5 M 2. How many km are in 4000 meters? 1000m1km=4000mXkm or 1000 m : 1 km :: 4000 m : X km 3. 1? 1km1000m=3.2kmXm or 1 km : 1000 m :: 3.2 km : X m

Objective 5

Dimensional Analysis

The concept of dimensional analysis involves manipulating the base unit to obtain the desired answer by canceling out the unwanted units. This is an advanced form of ratios and proportions and is commonly used when comparing measurements having different base units.

To use dimensional analysis concept, you must find the answers to three questions:

1. What are the original factors to convert?

2. What is the conversion formula or formulas?

3. What is the base unit of the answer?

STRATEGY 7-3: Dimensional Analysis

1. Read the question.

2. Identify what factors are to be converted.

3. Select the proper conversion formula or formulas.

4. Cancel unwanted units in a diagonal fashion.

5. Multiply across the problem.

6. Divide if necessary.

7. Label your answer with the desired base unit.

8. Check your answer.

Example:
3 feet = _______________ inches
1. Read the question. 3 feet is equal to _______________ centimeters. 2. Identify what factors are to be converted. 3 feet 3. Select the proper conversion formula or formulas. 12 inches = 1 foot 4. Cancel unwanted units in a diagonal fashion. 5. Multiply across the problem. 12×31=36 6. Divide if necessary. In this problem, division is not necessary because any fraction with 1 in the denominator represents a whole number. 7. Label your answer with the desired base unit. inches 8. Check your answer. 3 feet is equal to 36 inches.