# Conversions among Measurement Systems

• Convert among metric, household, and apothecary systems using ratio and proportion

• Convert among metric, household, and apothecary systems using dimensional analysis

## Introduction

In the previous chapter you learned the basic measurements found in the household, metric, and apothecary systems of measurements. Each of these is used today in prescribing and administering medications. Another measurement system, **avoirdupois,** is also available, but this system is not normally found in calculations or conversions. In this system, 16 ounces = one pound (7000 grains = one pound). Two other measures are used in dosage calculations—milliequivalents and units—that will be discussed in Chapter 6.

Conversions among the systems are only necessary if the two factors needed for calculation are not found within the same measurement system. If both factors are already in the metric system, then moving within the system is all that is necessary, as seen in Chapter 4. This is likewise true for the apothecary and household measurements. However, if one factor is in one system, such as the metric system, and the other factor is in another system, such as household, proportional equations are used to find the unknown approximation.

## Using Ratio and Proportion for Conversion of Units

Ratio is the relationship of one quantity to another, whereas proportion is the relationship between two equal ratios. In ratio and proportion, an unknown is solved using “*x*” as the unknown. This provides a logical and systematic means of finding the equivalent unknown when knowns are used for calculations. Two equal ratio sets (or the relationship between two equivalents, such as a [extreme] : b [mean] :: c [mean] : d [extreme]) is indicated for calculating proportional equivalents. When one of the equivalents is unknown, an “*x*” is used to indicate the unknown. (See Chapter 2 if you need to review this material.)

When the ratios have been properly aligned into proportion(s), multiply the two inside numbers (means, or “insies”) and the two outside numbers (extremes, or “outsies”) and then solve for “*x*.” Remember that what is done to numbers on one side of the equation must be done to numbers on the other side of the equation. If you need more review for ratio and proportion, refer to Chapter 2.

## Using Dimensional Analysis for Converting Among Units

1. Find the known, or given, quantity— c.

2. What is the desired, or wanted, amount?—*x* tablespoons.

3. What are the conversion factors that are needed to make the necessary calculation? In this case, we need to know that 2 tablespoons equals 1 oz and 8 oz equals 1 c.

4. Set up the problem with factors that are available for conversion factors. You want to cancel out like factors by placing them in a numerator of the first fraction followed by the denominator in the next fraction as follows:

5. Cross out the unwanted units. Just as with any other mathematical equation, if units appear in both the numerator and the denominator, you may cancel them to find the unit that is desired. In this case, the remaining unit is a tablespoon, which is the unit you are seeking.

6. Multiply the numerators, multiply the denominators, and divide the product of the numerators by the product of the denominators. This will give you the desired quantity that was originally your unknown factor.

So, after completing the problem:

Now let’s look at other examples found within the same measurement systems.

## Conversions Between Household and Apothecary Systems

The apothecary system has only a few significant measurements that, although not commonly used, do convert into household measurements. Of importance are minims to drops, drams to teaspoons, and ounces to tablespoons (Figure 5-1). Cups, pints, quarts, and gallons are used by both systems. Length is not found in the apothecary system, so the conversions are not included in Table 5-1. As the chapter unfolds, the metric system will be added to combined tables for conversions among measurement systems.

TABLE 5.1

Conversions between Apothecary and Household Systems of Measurement

PARAMETER | APOTHECARY UNITS | HOUSEHOLD UNITS | METRIC UNITS |

Volume | i (1 minim) | 1 gtt (1 drop) | — |

i (1 dram, 60) | 1 tsp (1 teaspoon) | — | |

( ounce) | 1 tbsp (1 tablespoon, 3 tsp) | — | |

i (1 oz) | 2 tbsp (2 tbsp, 6 tsp) | — | |

viii | 1 c (8 oz, 1 cup, pint) | — | |

1 pt (1 pint, 2 c, xvi) | 1 pt (1 pint, 2 c, 16 oz) | — | |

1 qt (1 quart, 2 pt, 4 c, 32) | 1 qt (1 quart, 2 pt, 4 c, 32 oz) | — | |

1 gal (4 qt, 8 pt, 16 c, 128) | 1 gal (4 qt, 8 pt, 16 c, 128 oz) | — | |

Mass/Weight | i (1 oz, 60 gr)* | 1 oz | — |

1# (1 lb, xii) | 1# or 1 lb (16 oz)* | — | |

Length | N/A | N/A | — |

^{*}Note that an apothecary pound contains only 12 oz, while a household pound contains 16 oz.