Review these relationships. When you are familiar with them, fill in the blanks.
Solutions.
A. 1 mg = 0.001 g (10−3g) = 0.000001 kg (10−6 kg) = 1000 μg (103 μg) = 1,000,000 ng (106 ng)
B. 1 kg = 1000 g (103 g) = 1,000,000 mg (106 mg) = 1,000,000,000 μg (109 μg)
C. 1 g = 1,000,000 μg (106 μg) = 1000 mg (103 mg) = 1,000,000,000 ng (109 ng) = 0.001 kg (10−3 kg)
3. If you got these right, move on to frame 4; if not, review and try again.
Fill in the blanks:
A. 1275 mg =_____g
B. 130 mg =_____μg
C. 0.032 g =_____mg
D. 455 mg =_____kg
E. 0.0075 g =_____μg
F. 0.030 mg =_____g
G. 8.8 × 105 μg =_____kg
H. 0.094 kg =_____g
I. 62 ng =_____mg
Solutions.
A. 1.275 g
B. 130,000 μg (or 1.3 × 105 μg)
C. 32 mg
D. 0.000455 kg (or 4.55 × 10−4 kg)
E. 7500 μg
F. 0.000030 g (or 3.0 × 10−5 g)
G. 8.8 × 10−4 kg
H. 94 g
I. 6.2 × 10−5 mg
If you had a perfect score, proceed. If you had trouble setting up your conversions, review Chapter 1. If you attempted the problems before learning the metric weight relationships, go back and study them. Check also Appendix 1. Do not go ahead in this chapter until you can do every problem presented above.
MEASUREMENT OF VOLUME
4. The standard unit of volume in the metric system is the liter (L). The following listing describes the metric units most frequently used by pharmacists in measuring volume and understanding clinical laboratory test values:
When you have learned the relationships above, fill in the blanks:
A. 1 mL =_____cc =_____L =_____μL
B. 1 L =_____μL =_____cc
C. 1 μL =_____mL =_____L
Solutions.
A. 1 mL = 1 cc = 0.001 L (10−3 L) = 1000 μL (103 μL)
B. 1 L = 1,000,000 μL (106 μL) = 1000 cc (103 cc)
C. 1 μL = 0.001 mL = 10−6 L
5. Now try these:
A. 2.6 mL =_____cc
B. 3.5 L =_____cc
C. 0.4 mL =_____μL
D. 0.1 μL =_____L
E. 6 mL =_____L
F. 2.37 L =_____mL
G. 0.072 cc =_____μL
Solutions.
A. 2.6 cc
B. 3500 cc = 3.5 × 103 cc
C. 400 μL
D. 0.0000001 L = 1 × 10−7 L
E. 0.006 L = 6 × 10−3 L
F. 2370 mL = 2.37 × 103 mL
G. 72 μL
If you had a perfect score, proceed to next frame. If you ran into trouble, review now to overcome any difficulties.
MEASUREMENT OF LENGTH
6. The meter (m) is the basic unit of length. The metric units of length most frequently encountered by pharmacists are as follows:
When you are familiar with the above, do these problems:
A. 170 cm =_____mm
B. 12.5 μm =_____mm
C. 0.2 cm =_____m
D. 0.32 m =_____mm
E. 0.013 m =_____cm
F. 744 μm =_____cm
G. 6.19 mm =_____nm
H. 0.08 m =_____μm
Solutions.
A. 1700 mm
B. 0.0125 mm
C. 0.002 m = 2 × 10−3 m
D. 320 mm
E. 1.3 cm
F. 0.0744 cm
G. 6.19 × 106 nm
H. 8 ×. 104 μm
If you had a perfect score, proceed. If not, be sure you understand how to do each problem before going any further.
7. The following problems will review metric system conversions. If you were able to get all of the problems in the previous sections right on the first try, you may skip the review and go to frame 8.
8. Despite the widespread utilization of the metric system, there are occasions when it is necessary to deal with quantities expressed in units from other systems of measurement. For example, these units might be occasionally used to describe drug dosage (in grains, gr) or a finished quantity of a prescription product (in ounces, oz or fluidounces, f). In those cases, we will have to convert the values from one unit system to another (refer to the common systems in Appendix 1).
The various systems have very different origins, and the relationships between units are usually not in terms of whole numbers. They are approximations expressed in enough significant figures to satisfy the particular application.
The United States Pharmacopeia (USP) states, for example, that
These relations, referred to as exact equivalents, are actually highly refined approximations. They are used when pharmaceutical formulas for commercially manufactured products are converted from one system to another. Conversions and other calculations for prescriptions do not require this high degree of accuracy. If a calculation is carried to three significant figures, the maximum error resulting from rounding is 0.5%. This is ample, considering that measurements for prescriptions are permitted a 5% tolerance. Consequently, for prescription compounding, the equivalents should be rounded to three significant figures:
According to the USP, 1 oz = 28.350 g. What conversion relationship should be used for:
A. Prescription work?
B. Pharmaceutical manufacturing?
Solutions.
A. 1 oz = 28.4 g
B. 1 oz = 28.350 g
9. Following is a collection of mathematical statements that allow conversion of weight among the metric, apothecary, and avoirdupois systems. They are rounded to three significant figures and are intended for use in prescription calculations.
Only the first two expressions may be memorized, since all of the others may be derived from them. However, it’s easy enough to memorize the others, thus reducing computation and saving time.
When you think you are sufficiently acquainted with the relationships, fill in the blanks.
A. 1 gr (avoirdupois) =_____gr (apothecary)
B. 1 kg =_____lb
C. 1 g =_____gr
D. 1 gr =_____mg
E. 1 lb =_____g
F. 1 oz =_____g
Solutions.
A. 1 gr (apoth.)
B. 2.20 lb
C. 15.4 gr
D. 64.8 mg
E. 454 g
F. 28.4 g
10. Statements of equivalence that allow conversion of volume units include:
Accuracy is to three figures, so these values are suitable for prescription calculations.
When you know these statements, fill in the blanks.
A. 1 f =_____cc
B. 1 pt =_____mL
C. 1 qt =_____L
Solutions.
A. 29.6 mL = 29.6 cc
B. 473 mL
C. 1 qt = 2 pt = 946 mL = 0.946 L
11. Here are some problems that require conversion from one system of measurement to another. Use them for practice.
A. How many milligrams of nitroglycerin are there in 60 tablets if each tablet contains 1/100 gr of nitroglycerin?
B. Convert 1 qt to microliters.
C. If an ounce of papaverine costs $3.75, how many dollars would 146 gr cost?
D. Convert 60 g to grains.
E. Convert 6f to milliliters.
F. If 1 lb of an ointment costs $6.30, what is the cost of 60 g of the ointment?
Solutions.
A. 38.9 mg
B. 9.46 × 105 μL
C. $1.25. The “ounce” was avoirdupois.
D. 924 gr
E. 178 mL
F. 83¢
12. Sometimes it will be necessary to convert several quantities to other units of a different system. This is a rare situation. Here is an example.
A syrup contains 12.0 gr of a pain reliever in each fluidounce. How many milliliters contain 650 mg?
Solution. 24.7 mL
CALCULATIONS
One way to attack this problem is first to find the number of milligrams per fluidounce and then use proportion to calculate the number of milliliters.
13. There is a table in the USP that lists approximate equivalents. The relationships given in that table are not to be used when calculating quantities of materials that will be weighed or measured for a prescription. However, when a prefabricated dosage form (one prepared by a pharmaceutical manufacturer) is prescribed in one system of units but is available to the pharmacist in strengths given in a different system, it is permissible to dispense the strength that is approximately equivalent to that prescribed.
A pharmacist receives a prescription for tablets containing aminophylline, 1 gr (which is equivalent to 97.2 mg). He has on hand aminophylline, 100 mg. What should he do?
It is permissible to dispense aminophylline tablets, 100 mg, when tablets are written for 1 gr.
Some examples of approximate equivalents:
The following problems exemplify some practical uses of the metric system in pharmacy practice. Use them to iron out any weak spots in your work.
A. How many milliliters of oil are needed to prepare 640 capsules if 15 capsules contain 137 μL of oil?
B. How many kilograms of sodium fluoride are needed to make 60,000 tablets of sodium fluoride tablets each containing 50 μg?
C. You have 15.8 g of tetracycline hydrochloride powder. How many 250-mg capsules can you make from this quantity of powder?
D. A pharmacist adds sufficient water to a vial containing 2 million units of penicillin to make a total volume of 5 mL of penicillin suspension. How many milliliters of the suspension should be injected into a child who is to receive a dose of 300,000 units?
E. A soft gelatin capsule contains 0.22 mL of an oil. How many liters of oil would be required for 4500 capsules?
F. How many tablets each containing 2.5 mg of amphetamine can be made from 0.620 kg of amphetamine?
G. How many micrograms of vitamin A are there in each tablet if 2.75 g of vitamin A are used to make 5000 tablets?
H. A manufacturer fills 490 bottles so that each bottle contains 30 mL of an oil. If he started with 15.5 L of the oil, how many milliliters are left after the filling operation is complete?
I. If 12.0 mg of a drug are present in 440 g of a powder, how many grams of drug would there be in 14.0 kg of powder?
Solutions.
A. 5.85 mL
B. 0.003 kg
C. 63 capsules
D. 0.75 mL
E. 0.99 L
F. 2.48 × 105 tablets
G. 550 μg
H. 800 mL
I. 0.382 g
CLASS A PRESCRIPTION OR TORSION BALANCE: MINIMUM WEIGHABLE AND MEASURABLE QUANTITIES
14. The balance used in weighing drugs for prescription compounding is known as a Class A or torsion balance. It is a fairly sensitive instrument. In a prescription balance that meets current standards, the sensitivity requirement (SR) is 6 mg. This means that a load of 6 mg causes a deflection of at least one scale division of the pointer. The balance is therefore capable of discriminating a minimum difference of 6 mg. This amount represents the maximum error in weighing that will be incurred using a prescription balance in proper working order. To calculate the percent error divide the sensitivity requirement by the amount to weigh and express the result as percent.
If 1500 mg are weighed, = 0.004 = 0.4%
If 150 mg are weighed, = 0.04 = 4%
and so on.
Table 2.1 shows how the percent error changes depending on the amount that is weighed. Since the maximum percent error that is acceptable in weighing for prescription compounding is 5%, we see that it is all right to use the prescription balance to weigh 1500 mg or 150 mg but that the percent error involved in weighing 15 mg is much too great.
TABLE 2.1Effect of amount weighed on percent error
Amount weighed (mg)
SR or error (mg)
% error
1500
6
0.4
150
6
4
15
6
40
Just as with a cylindrical graduate, the percent error increases as the amount weighed becomes smaller. From these data, we can tell that somewhere between 150 mg and 15 mg a particular quantity exists such that the error in weighing would be exactly 5%. That quantity is the smallest amount that can be weighed on a prescription balance with acceptable accuracy.
For example, the minimum weighable quantity for a prescription balance with a sensitivity requirement of 6 mg and 5% maximum acceptable percent error could be calculated by:
Let j equal minimum weighable quantity:
This calculation shows that if a quantity of 120 mg or more is weighed on a prescription balance, the error will be 5% or less. The accuracy will therefore be acceptable. If less than 120 mg of a drug is required, direct weighing of that quantity on a prescription balance will lead to unacceptably large errors. Other techniques must be used. These are discussed below under aliquot method.
Now, try these problems.
A. What is the maximum percent error incurred if a balance with a sensitivity requirement of 15 mg is used to weigh 120 mg of a powder?
). In those cases, we will have to convert the values from one unit system to another (refer to the common systems in Appendix 1).
=_____cc
to milliliters.
gr (which is equivalent to 97.2 mg). He has on hand aminophylline, 100 mg. What should he do?
gr.
= 0.004 = 0.4%
= 0.04 = 4%
