Fractions, Decimals, & Percentages #2

Military Time

12-hour clock 24-hour clock Noon 12:00 1 p.m. 13:00 2 p.m. 14:00 3 p.m. 15:00 4 p.m. 16:00 5 p.m. 17:00 6 p.m. 18:00 7 p.m. 19:00 8 p.m. 20:00 9 p.m. 21:00 10 p.m. 22:00 11 p.m. 23:00

Metric System

The major system of weights and measures used in medicine is the metric system. It was developed in France in the late 18th century and is based on a decimal system. That is, different measurement units are related by measures of ten. Technicians need to know metric measures for both liquids and solids.

Household Units

The teaspoon & tablespoon are common household measurement units that are regularly used in liquid prescriptions.

Converting between Decimals & Percent's

Percent's are a special kind of fraction (part of a whole) where the whole is 100. Percent is represented by the symbol %. 25% means 25 parts of 100. 25 parts of 100 can also be written as a decimal fraction of 0.25.

Interpreting Common Pharmacy Sigs

Sig Meaning 1. i tab b.i.d. Take 1 tablet twice a day 2. i tab t.i.d. Take 1 tablet 3 times a day 3. i tab q.i.d. Take 1 tablet 4 times a day 4. i tab q.o.d. Take 1 tablets every other day 5. i tab a.m. Take 1 tablet in the morning 6. i tab h.s. Take 1 tablet at bedtime 7. i tab a.c. Take 1 tablet before meals 8. i tab p.c. Take 1 tablet after meals

Dosing Schedules

Used to provide instructions for what quantity of a drug should be taken how it's to be administered, and how often. - The dose is the amount of drug taken at a time. Doses are expressed in different ways. Most commonly, the dose is given as the # of dosage forms (e.g., 1 tablet, 1 capsule, 1 suppository) or some other quantity (e.g., 2 puffs). Doses are sometimes given as the weight of the drug (e.g., 250 mg) or the volume of a drug solution or suspension (e.g., 10mL, 2 drops).

Solids

(pills, granules, ointments, etc.) are measured by weight.

Safety Tips (Continued)

- Always take extra precautions when calculating doses for infants and children. - Always take extra precautions when calculating doses for high-alert medications. - If you are not certain about how to do a calculation, check with the pharmacist. - Take extra care when converting units in the metric system. Tenfold or hundredfold errors can happen easily, and can be satastrophic.

Safety Tips

- Before performing a calculation, first estimate the amount you are likely to need. This will give you an idea of what your calculated answer should be. - Commercials drug formulations are generally available in doses that are commonly administered. Anytime you have calculated that a dose is more than one or two tablets, or one or two capsules, or one vial or ampule of an injectable medication, take extra steps to be sure you didn't make a mistake. - Doses of oral liquid medicines are usually 5 mL or less for children, and 5 to 20 mL for adults. If a dose seems unusually large, check to be sure you didn't make a mistake.

Example - Converting from Decimals to Percent's

0.25 = 25% To convert from decimals to percent's, move the decimal point to the right 2 places and add the % sign.

Conversions

1 L = 33.8 fl oz. 1 oz. = 28.35 g 1 pt. = 473.167 mL 1 g = 15.43 gr 1 fl oz. = 29.57 mL 1 gr = 64.8 mg 1 kg = 2.2 lb. 1 tsp = 5 mL 1 lb. = 453.59 g 1 tbsp = 15 mL

Answers(1-6)

1. 7,000 mcg 2. 3,200 mg 3. 0.0648 g 4. 30 mL 5. 300 mL 6. 7,000 g

Answers(1-6)

1. 0.1 g = 0.001 kg 2. 5,000 mg = 0.005 kg 3. 2,000 g = 2,000,000 mg 4. 5 g = 0.005 kg 5. 25,000 mg = 0.025 kg 6. 30,000 g = 30,000,000 mg

Answers (1-5)

1. 10% 2. 35% 3. 50% 4. 75% 5. 80%

Answers(1-5)

1. 30 2. 10 3. 10 4. 10 5. 90

Answers (1-6)

1. mcg 2. L 3. mL 4. g 5. mg 6. kg

Military Time

12-hour clock 24-hour clock Midnight 00:00 1 a.m. 01:00 2 a.m. 02:00 3 a.m. 03:00 4 a.m. 04:00 5 a.m. 05:00 6 a.m. 06:00 7 a.m. 07:00 8 a.m. 08:00 9 a.m. 09:00 10 a.m. 10:00 11 a.m. 11:00

Example - Converting from Percent's to Decimals

25% = 0.25 To convert from percent to a decimal fraction, move the decimal point to the left 2 places & remove the % sign.

Answers (6-10)

6. 0.15 7. 0.3 8. 0.4 9. 0.6 10. 0.7

Answers (7-12)

7. 1,000 g 8. 1,000 mcg 9. 129.6 mg 10. 1,000mL 11. 0.001 L 12. 0.001 g

Answers (7-12)

7. 437.5 gr 8. 1.1 lb. 9. 2 tsp 10. 1 tbsp 11. 32 F 12. 0.25 L

Example - Calculating Days Supply Using Dimensional Analysis

A prescription reads: amoxicillin 250 mg, #30, one capsule orally, three time a day. Question: What is the days supply? Step 1: Identify the relevant numerical relationships and conversions (the facts). a. 1 capsule/dose b. 3 doses/day c. 30 capsules/prescription Step 2: Set up a dimensional analysis equation so the undesired units (dimensions) cancel out when the fractions are multiplied and the desired unit is in the numerator. day dose 30 capsules ___________ x _____________ x __________________ 3 doses 1 capsule prescription Step 3: Solve the equation. 10 days __________________ prescription

Example - Filling a Capsule Prescription Using Dimensional Analysis

A prescription reads: amoxicillin 250 mg, one capsule orally, three times a day for seven days. Question: How many capsules will be needed to fill this prescription? Step 1: Identify the relevant numerical relationships and conversions (the facts). a. 1 capsule/dose b. 3 doses/day c. 7 days/prescription Step 2: Set up a dimensional analysis equation so the undesired units(dimensions) cancel out when the fractions are multiplied and the desired unit is in the numerator. 1 capsule 3 doses 7 days _______________ x ______________ x __________________ dose day prescription Step 3: Solve the equation. 21 capsules ____________________ prescription

Example - Converting Fahrenheit to Celsius

C temperature = 59 x (number of degrees F - 32) Question: What is 212 F in Celsius? Answer: 5/9 x (212 - 32) = 5/9 x 180 = 100 F *****Note that the temperature of water freezing is 0 C and 32 F. *****

Practice Problems - Calculating Days Supply

Calculate the days supply for each of the following prescriptions: 1. Atenolol 50 mg #30 Sig: i tab a.m. = 2. Ciprofloxacin 500 mg #20, Sig: i tab b.i.d. = 3. Cephalexin 500 mg #30 Sig: i cap t.i.d. = 4. Penicillin VK 500 mg #40 Sig: i tab q.i.d. = 5. Hydrochlorothiazide 50 mg #90 Sig: i tab daily a.m. =

Practice Problems - Converting Between Decimals & Percent's

Convert the following decimals to percent's: 1. 0.10 = 2. 0.35 = 3. 0.5 = 4. 0.75 = 5. 0.8 =

Practice Problems - Converting Between Decimals & Percent's

Convert the following percent's to decimals: 6. 15% = 7. 30% = 8. 40% = 9. 60% = 10. 70% =

Practice Problems - Converting with Multiple Units

Convert these Numbers: 1. 100 mg = 2. 5 g = 3. 2 kg = 4. 5,000 mg = 5. 25 g = 6. 30 kg =

Practice Problems - Conversions

Convert these numbers: 7. 1 oz. = 8. 0.5 kg = 9. 10 mL = 10. 15 mL = 11. 0 C = 12. 250 mL =

Practice Problems- Conversions

Convert these numbers: 1. 7 mg = 2. 3.2 g = 3. 1 gr = 4. 2 tbsp = 5. 0.3 L = 6. 7 kg =

Practice Problems - Metrics

Convert these units to equivalents: 7. 1 kg = 8. 1 mg = 9. 2 gr = 10. 1 L = 11. 1 mL = 12. 1 mg =

Daily Supply

Especially in the community pharmacy setting, technicians often need to be able to calculate how long the prescription should last the patient when taken as prescribed, i.e., the days supply.

Interpreting Common Pharmacy Sigs

Interpret as 1. 1 tablet/dose X2 doses/day = 2 tablets/day 2. 1 tablet/dose X3 doses/day = 3 tablets/day 3. 1 tablet/dose X4 doses/day = 4 tablets/day 4. 1 tablet/dose X1/2 dose/day = 1/2 tablet/day 5. 1 tablet/dose X1 dose/day = 1 tablet/day 6. 1 tablet/dose X1 dose/day = 1 tablet/day 7. 1 tablet/dose X3 doses/days = 3 tablets/day 8. 1 tablet/dose X3 doses/day = 3 tablets/day

Liquids

Liquids (including lotions) are measured by volume. The most widely used metric volume measurements are liters or milliliters.

Practice Problems - Metrics

Provide the abbreviation for these: 1. Microgram = 2. Liter = 3. Milliliter = 4. Gram = 5. Milligram = 6. Kilogram =

Example - Converting Celsius to Fahrenheit

Question: What is 100 C in Fahrenheit? Answer: 1 4/5 x 100 = 180 and 180 + 32 = 212 F

Example - Converting mL into Fluid Ounces Using Dimensional Analysis

Question: You have a prescription for 120 mL of theophylline liquid and want to know how many fluid ounces is equal to 120 mL. Step 1: Identify the relevant numerical relationship and conversions (the facts). a. 120 mL theophylline liquid/prescription (numerical relationship b. 1 fluid ounce/29.57 mL (conversion) Step 2: Set up a dimensional analysis equation so the undesired units (dimensions) cancel out when the fractions are multiplied and the desired unit is in the numerator. 1 fluid ounce 120mL ___________________ x __________________ 29.57 mL prescription Step 3: Solve the equation. 4 fluid ounces (rounded)/prescription

Apothecary System

Sometimes used in prescriptions, primarily with liquids. Includes the fluid once, pint, quart, and gallon.

Avoirdupois System

System of weight (ounces and pounds) that we commonly use. However, 1 avoirdupois unit used in pharmacy is rarely used elsewhere. It's the grain.

Temperature

The Celsius scale, which is also called centigrade is used to measure temperature. The relationship of Celsius (C) to Fahrenheit (F) is: F temperature = (9/5 times # of degrees C) + 32

Dosing Schedules (Continued)

The administration of drugs at the correct time, as prescribed, is very important. To avoid confusion between a.m. and p.m. times, sometimes military times are given. Military times use a 24-hour clock instead of commonly used 12-hour clock. In military time, the day starts at midnight.

Dosing Schedules (Continued)

The dosing regimen is the frequency at which the drug doses are given (e.g., 5mL twice a day, 1 tablet 3 times a day). Sometimes the dosing frequency is given in terms of hours (e.g., every 6 hours, every 8 hours, every 12 hours, etc.). The total daily dose can be determined from the dose and the number of times per day the dose is administered.

The Grain

The grain is the same weight in several different measurement systems: apothecary, avoirdupois, and troy. It's said to have been established as a unit of weight in 1266 by King Henry III of England when he required the English penny to weigh the equivalent of 32 dried grains of wheat. On the metric scale, one grain equals 64.8 milligrams. However, this is often rounded to 65 milligrams.

Dimensional Analysis

There are 3 main ways to solve pharmaceutical calculations: dimensional analysis; equations, & variables(algebra); & ratio and proportion. Dimensional analysis, also called the factor/label method, can be used to solve the most calculations in the pharmacy. To start, identify the known numerical relationships associated with the dosing schedule. Also identify any conversions that may be needed if all measurements don't have the same units(dimensions). The numerical relationships associated with the dosing schedule as well as the conversions are expressed as fractions. The fractions are arranged so that dimensional units appear in both numerators and denominators in a way that allows undesired units to cancel out when the fractions are multiplied.

Measurement

There are different systems of measurement used in pharmacy: Metric, English, Apothecary, & Avoirdupois. The Metric System is the primary system used. Within these systems there are different measurements for weight, volume, & length, as well as for liquids & solids. There are also different measurement systems for temperature. It's necessary to know how to perform conversion--i.e., how to convert q type of measurement to another so that both amounts are equal.

Household Conversions

Unit Abbreviation Conversion Teaspoon tsp 1 tsp = 5mL Tablespoon tbsp 1 tbsp = 3tsp = 15 mL Cup cup 1 cup = 8 fl oz.

Apothecary Conversions

Unit Symbol Conversions Gallon gal 1 gal = 4 qt Quart qt 1 qt = 2 pt. Pint pt. 1 pt. = 16 fl oz. Ounce fl oz. 1 fl oz. = 8 fl dr Fluid Dram fl dr 1 fl dr = 60 min Minim min or Mx.

Avoirdupois Conversions

Unit Symbol Conversions Pound lb. 1lb = 16 oz. Ounce oz. 1 oz. = 437.5 gr Grain gr 1 gr = 64.8 mg

Measurements

Unit Symbol Liquid Conversions Liter L 1 L = 10dL = 1,000 mL Deciliter dL 1dL = 0.1 L = mL Milliliter mL 1mL = 0.001 L = 0.01 dL Note: Deciliters are rarely used in pharmacy, but are included here for reference and to illustrate the decimal relationship of these measures.

Solid Conversions

Unit Symbol Solid Conversions Kilogram kg 1kg = 1,000 g Gram g 1g = 0.001kg = 1,000mg Milligram mg 1mg = 0.001g = 1,000mcg Microgram mcg or ug 1mcg=0.001mg=0.000001g

Example - Preparing an Intravenous Solution of Potassium Chloride

You are preparing an intravenous solution(IV) that requires the addition of potassium chloride (KCl). You have a vial of KCl containing a concentration of 20 mEq per 10 mL. Question: How many mL of this solution should you add to the IV if the IV should have a total of 50 mEq of KCl in it? Step 1: Identify the relevant numerical relationships and conversions(the facts). a. 20 mEq/10 mL b. 50 mEq/prescription Step 2: Set up a dimensional analysis equation so the undesired units (dimensions) cancel out when the fractions are multiplied and the desired unit is the numerator. 10 mL 50mEq ___________ x __________________ 20 mEq prescription Step 3: Solve the equation. 25 mL _________________ prescription