Pharmacy for Technicians: Seventh Edition

6.7 Converting Other Systems to Metrics

Due to safety reasons, the avoirdupois and apothecary systems have been almost completely phased out. However, occcasionally home dosage or medication orders are written in the household system. To convert any other system to metrics, first convert the units into decimals, and then apply the conversion amounts listed in Table 6.9.

The volume held by a household teaspoon may vary, which is why it is not used for pharmaceutical measurements, but a true teaspoon equals 5 mL.

Rounding Off Decimal Conversions

To simplify and standardize conversions, pharmacy practice rounds the conversion rates up or down. For example, when converting from fluid ounces to milliliters, it is common practice to round 29.57 mL to 30 mL, as has been explained earlier. But remember, the discrepancy becomes much larger when measuring large amounts of fluid ounces and rounding them off.

Consider the situation when converting a household pint (16 fl oz). When you multiply the rounded-off 30 mL by 16, it equals 480 mL. This calculation becomes problematic because the more exact 29.57 mL multiplied by 16 is equal to only 473.12 mL—a difference of almost 7 mL! However, bottled solutions are often put in 8 or 16 fl oz containers and usually dosed out in 30 mL increments. So you may use the rounded 30 mL value for a fluid ounce and the rounded 480 mL for a pint when performing pharmacy calculations for this chapter.

Another calculation problem can occur with the ounce. The apothecary ounce is a weight measure and not a liquid measure. The ounce unit has been rounded down (from 31.1 g to 30 g) in the apothecary system and rounded up (from 28.35 g to 30 g) in the avoirdupois system, so they both use 30 g. Today, some physicians still occasionally write prescription orders for liquid dosage forms in ounces.

As explained earlier, the grain unit also poses accuracy and safety problems and has different conversion rates. Most pharmacists consider 1 gr to be equal to 65 mg, but manufacturers often use a 60 mg conversion for 1 gr. In most cases, this difference in measurement is not clinically significant. However, for premature infants and neonates, precise calculations and uniform measurements must be used.

While slight differences in metric conversions do exist, the use of standardized metric equivalents aid greatly in accurate medication dosing and safe patient care. Pharmacy technicians should confer with the pharmacist if in doubt about any conversions to metric equivalents to ensure that the correct conversion rate is selected.

Table 6.9 Household and Avoirdupois/Apothecary Measurements

Measurement Unit	Equivalent within System	Metric Equivalent
Avoirdupois System
1 gr (grain)	–	65 mg
1 oz (ounce)	437.5 gr	30 g (28.35 g)*
1 lb (pound)	16 oz or 7,000 gr	454 g
Household System
Volume 1 tsp (teaspoon)	–	5 mL
1 tbsp (tablespoon)	3 tsp	15 mL
1 fl oz (fluid ounce)	2 tbsp	30 mL (29.57 mL)**
1 cup	8 fl oz	240 mL
1 pt (pint)	2 cups	480 mL
1 qt (quart)	2 pt	960 mL
1 gal (gallon)	4 qt	3,840 mL
Weight 1 oz (ounce)	–	30 g
1 lb (pound)	–	454 g
2.2 lb	–	1 kg

* An avoirdupois ounce actually contains 28.34952 g; however, that number is usually rounded up to 30 g. It is common practice to use 454 g as the equivalent for a pound.

** In reality, 1 fl oz (household measure) contains less than 30 mL; however, 30 mL is usually used. When packaging a pint, companies will typically present 473 mL rather than the full 480 mL, thus saving money over time.

Using Unit Cancellation to Calculate Conversions

When converting to measurement units of different dimensions (time, temperature, volume), you will often use a process known as dimensional analysis calculation. This is a very intimidating name for a very simple process that uses techniques you already know: multiplying by fractions of one and canceling elements out that balance each other. In fact, dimensional analysis is often considered an accurate shortcut, cutting out extra steps to get to the same end.

Name Exchange

Dimensional analysis calculation is also known as unit cancellation because it cancels out the measuring units of the known dimensions. The method is also called calculation by cancellation, unit label method, or factor label method.

You already know that if you multiply anything by 1, the amount stays the same. So if you are trying to convert pounds into kilograms, you multiply the pounds by a fraction that represents one as the single unit of 1 kg/2.2 lbs.

In dimensional analysis, you must set up the problems so that the starting units cancel one another out and you are left with the desired units. This is why dimensional analysis is also called “unit cancellation” or calculation by cancellation.

$starting units \times \frac{desired units}{starting units} = desired units$

Using dimensional analysis, calculate the number of minutes in one hour. The desired units (the units you want to find) are minutes and the starting units (the units you are given) are hours.

$1 hour \times \frac{60 minutes}{1 hour} = 60 minutes$

The starting units of hours are canceled out and leave the desired units as minutes.

Example 16

Consider you have the following prescription.

images Acetaminophen 400 mg

However, the stock bottle measures the drug only in grains. How many grains of acetaminophen are prescribed?

Step 1

Look up the conversion rate for grains to milligrams. Table 6.9 shows the conversion rate is 1 gr = 65 mg. Set up your equation so that the starting units cancel out (in this example, milligrams).

$400 mg \times \frac{1 gr}{65 mg} = 6.1537 gr$

Step 2

Round this down to the nearest whole number as grains cannot be split. This means 6 gr should be measured and used in the prescription. If you have tablets of 3 gr each, you will need two tablets per dose.

The conversion above could also have been done as a ratio and proportion equation using the butterfly technique of multiplying the means and extremes and then cancelling measurement units to come up with the same answer. You could have written the first equation as a proportion and gone from there:

$\frac{y g r}{400 m g} = \frac{1 g r}{65 m g}; so y g r \times 65 m g = 400 m g \times 1 g r$

$y gr = \frac{400 mg \times 1 gr}{65 mg} = 6.1538 gr; rounded to 6 gr$

In conversions, you can use the ratio and proportion approach to check the dimensional analysis answer and vice versa.

Example 17

You are to dispense 300 mL of a liquid preparation. If the medication amount (the dose) is 2 tsp, how many doses will there be in the final preparation?

Step 1

Begin setting up this problem with all the known information and the conversion value in Table 6.9, which is 1 tsp = 5 mL.

$1 dose = 2 tsp \times \frac{5 mL}{1 tsp} = 10 mL$

Step 2

In simple math, you ask how many times does 10 mL go into 300 mL? Take 300 mL and divide by 10 mL per dose for y doses to come up with 30 doses.

You can also complete this calculation using dimensional analysis, either in one step or multiple steps. Both examples are shown below.

One-step method:

$300 mL \times \frac{1 tsp}{5 mL} \times \frac{1 dose}{2 tsp} = 30 doses$

Multiple-step method:

Step 1

Calculate the number of milliliters per dose.

$\frac{2 tsp}{1 dose} \times \frac{5 mL}{1 tsp} = \frac{10 mL}{1 dose}$

Step 2

Calculate the number of doses in 300 mL.

$300 mL \times \frac{1 dose}{10 mL} = 30 doses$

Practice Tip

The oral dosage forms for nitroglycerin often come in proportions of $\frac{1}{200 gr}$ , $\frac{1}{150 gr}$ , and $\frac{1}{100 gr}$ .

Example 18

A patient receives the following prescription.

images 60 mL of medication in prefilled hypodermic syringes

There are 3 L of the solution available. How many hypodermic syringes can be filled with the available solution?

You can figure this out using dimensional analysis in either one or multiple steps.

One-step method:

$3 L \times \frac{1, 000 mL}{1 L} \times \frac{1 syringe}{60 mL} = 50 syringes$

Multiple-step method:

Step 1

Convert 3 L to milliliters.

$3 L \times \frac{1, 000 mL}{1 L} = 3, 000 mL$

Step 2

Use the calculated volume to determine the number of doses.

$3, 000 mL \times \frac{1 syringe}{60 mL} = 50 syringe$

Example 19

A physician prescribes the following order.

images 0.8 mg of nitroglycerin

The available supply has tablets containing 1/150 gr nitroglycerin. How many tablets should be given to the patient?

You can figure this out using dimensional analysis in either one or multiple steps. Table 6.9 says 1 gr = 65 mg. Remember we are told that 1 tablet = $\frac{1}{150}$ gr. It is easiest to approach this problem by calculating $\frac{1}{150}$ gr.

$1 tablet \times \frac{1}{150} gr = 0.0067 gr$

One-step method:

$0.8 mg \times \frac{1 gr}{60 mg} \times \frac{1 tablet}{0.0067 gr} = 1.83 tablets, rounded up to 2 tablets$

Multiple-step method:

Step 1

Calculate the number of grains in 0.8 mg.

$0.8 mg \times \frac{1 gr}{65 mg} = 0.0123 gr$

Step 2

Convert 0.0123 gr to tablets.

$0.0123 gr \times \frac{1 tablet}{0.0067 gr} = 1.84 tablets, rounded up to 2 tablets$

Remember, when multiplying with equivalent ratio fractions to solve medication-dosing problems, both numerators must be in the same units and both denominators must be in the same units. For example, in oral medications, the active ingredient is usually expressed in milligrams (mg), and the solution is expressed in milliliters (mL).

Incorrect:	$\frac{1.5 g}{100 ml} = \frac{400 mg}{y mL}$
Correct:	Convert the grams to milligrams: 1.5 g × 1,000 = 1,500 mg and then simplify.

$\frac{1500 m g}{100 m l} = \frac{400 m g}{y m L}$ You can then use the butterfly technique.

15y mL = 400 mL; then $y mL = \frac{400}{45} = 26.666 \dots$ rounded to 26.7 mL