# Systems of measure

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## Chapter: Pharmaceutical Drugs and Dosage: Pharmacy math and statistics

The metric system of measurements is based on the principle of multiples of 10 to define different ranges of quantities.

Systems of measure

The metric system of measurements is based on the principle of multiples of 10 to define different ranges of quantities. Prefixes in the metric sys-tem indicate that the mentioned numeric value be multiplied by nth power of 10. For example, the represented multipliers for the common prefixes are as follows: nano (prefix: μ) is 10−9, micro (prefix: μ) is 10−6, milli (prefix: m) is 10−3, centi (prefix: c) is 10−2, deci (prefix: d) is 10−1, deca (prefix: dk) is 101, hecto (prefix: h) is 102, and kilo (prefix: k) is 103. Therefore, 1 kg = 1,000 g = 1,000,000 mg = 1,000,000,000 μg = 1,000,000,000,000 ng.

In addition, the avoirdupois system (e.g., ounces and pounds) is the com-monly used system in everyday life, and the apothecary system (meaning pharmacy) (e.g., quarts and pints) is commonly used in the practice of pharmacy.

·           In the avoirdupois system, weight is expressed in grain (gr), ounce (oz), and pound (lb). The interconversions between these units and their relationship to the metric system are as follows:

kg = 2.2 lb

lb = 16 oz

oz = 437.5 gr = 28.4 g

gr = 65 mg

·           In the apothecary system, volume is expressed in the units of fluid dram (dr), fluid ounce (oz), pint (pt), quart (qt), and gallon (gal). The interconversions between these units and their relationship to the metric system are as follows:

1 gal = 4 qt = 3,785 mL

1 qt = 2 pt = 946 mL

1 pt = 16 oz = 473 mL

1 oz = 30 mL (more accurately, 29.57 mL)

3 (fluid dram) = 5 mL

Therefore, the sign “ʒ” appearing in the sign of the prescription as “ʒi” indicates 1 teaspoonful (tsp) or 5 mL. Note that 1 tablespoon is 15 mL and is symbolized as “ʓss” in the prescription. Similarly, the dispensing instruc-tion “ʓV” means to dispense 5 fʓ or 150 mL.

The laws of ratios and proportions can be used to interconvert units dur-ing calculations. For example, to convert 2.5 mg/5 mL into g/gal:

Ratio and proportion can also be used for the reduction and enlargement of formulas for dispensing the required quantity of a prescription. In addition, a conversion factor can be derived, which then becomes the multiplier for every ingredient in the formulation to dispense a given quantity.

Conversionfactor = Volume tobedispensed / Volumein the(unit) formula

For example, to dispense 200 mL of a prescription with a unit formula for 5 mL quantity, the conversion factor would be 200/5 = 40. Therefore, the quantity of every ingredient would be multiplied by 40 to make a 200-mL dispensed quantity.

## Volume and weight interconversions

The interconversions of weight and volume are useful in pharmacy dispens-ing to aid accuracy of measurement. Interconversions of weight for volume of liquids can be done using their density, which is weight per unit volume. Therefore, 1 mL of glycerol, of density 1.26 g/mL at room temperature, is equivalent to 1.26 g of glycerol. Alternatively, 1 g of glycerol is 1/1.26 = 0.79 mL of glycerol. Note that 1 cubic centimeter (cc or cm3) volume = 1 mL.

Sometimes, the information on specific gravity of a substance is avail-able, which can be used to perform similar calculations. Specific gravity is the ratio of weight of a substance to the weight of an equal volume of distilled water at 25°C. Therefore, it does not have any units. Since 1 mL of water = 1 g of water at 25°C, specific gravity represents the number of grams of a substance per unit volume of that substance in mL at 25°C. Density, on the other hand, is usually determined at ambient temperature or at the temperature at which measurements are to be made.

## Temperature interconversions

Interconversions of temperature between the Celsius (sometimes also known as centigrade), Fahrenheit, and Kelvin scales can be carried out using the following equations:

Interestingly, −40°C = −40°F.

At temperatures less than −40°C, °F < °C.

At temperatures greater than −40°C, °F > °C.

Although the Celsius and Fahrenheit scales are more commonly encountered in routine use, the Kelvin scale is used more commonly in the derivation and use of scientific equations.

## Accuracy, precision, and significant figures

Accuracy represents the degree of closeness of a measurement to the desired, target, or actual quantity. Thus, if the target quantity to be weighed is 125 mg and the actual weighed quantities are 121 and 123 mg in two different trials, the latter would be considered more accurate than the former. Accuracy is a measure of distance from the target.

Precision, on the other hand, represents the reproducibility or repeatabil-ity of a measurement. It represents the relative closeness of individual mea-surements to the average of these measurements when the measurements are carried out more than once. Precision is an indication of variability of a measurement or, said differently, of the confidence in the exactness of a measurement. For example, a balance that can weigh ±0.01 g of a target weight would lead to a more precise measurement than a balance that weighs ±0.1 g of the target weight. In pharmacy practice, both accuracy and precision are needed.

Significant figures, or the number of digits in the decimal places, repre-sent the precision of a measurement by indicating the least amount that could be measured. For example, a weight of 1.0 g represents ±0.1 g preci-sion of the balance on which the weight was taken. Thus, the actual weight of the substance that is labeled as 1.0 g could be anything in the range of 0.9–1.1 g (a range of 0.2 g). Similarly, a recorded weight of 1.000 g rep-resents ±0.001 g precision of the balance on which the weight was taken. Thus, the actual weight of the substance that is labeled as 1.000 g could be anything in the range of 0.999–1.001 g (a range of 0.002 g).

The concept of significant figures is utilized in rounding off consider-ations. For example, numerical calculations of quantities can introduce additional digits at the tailing end of the calculated number. These numbers should then be rounded off to the significant digits of original measurement when communication of precision is important. For example, splitting a tablet labeled 125 mg has the precision of dose measurement of ±1 mg. When this tablet is split in half, each half can be considered to contain 125/2 = 62.5 mg of the drug. However, the number 62.5 mg indicates a precision of ±0.1 mg, which does not accurately represent the precision of dose measurement.