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I. Prefixes and their values: a. Micro (mc) [write out microgram] i. Millionth ii. 1 microgram = 0.000001 gram iii. 1 microgram = 0.001 milligram
- 1,000 micrograms = 1 milligram = 0.001 gram
- 500 micrograms = 0.5 mg = 0.0005 gram b. Milli (m) i. Thousandth ii. 1 milligram = 0.001 gram
- 1,000 milligrams = 1 gram c. Centi (c) i. Hundredth ii. 1 centimeter = 0.01 of a meter
- 100 centimeters = 1 meter d. Deci (d) i. Tenth ii. 1 deciliter = 0.1 Liter
- 10 deciliters = 1 Liter e. Deka (da) i. Tens ii. 1 dekagram = 10 grams f. Hecto (h) i. Hundreds ii. 1 hectogram = 100 grams g. Kilo (k) i. Thousands ii. 1 kilogram = 1,000 grams
The prefixes that you will deal with the most in performing medication calculation problems are milli- (milligrams, milliliters), micro- (micrograms), and kilo- (kilograms). The conversions that you will use most often are bolded. Commit these to memory.
II. Rounding
For purposes of rounding your dose, calculate to the next decimal place beyond the figure you are rounding to. For example, to round to the nearest tenth, calculate to the hundredths decimal place. If the last calculated decimal place is 5 or greater, round the decimal place to the left up. To avoid over or under dosing your patient, never round liquid medications to the nearest whole number; use a syringe with the appropriate calibrations to measure an exact dose. Round to the smallest unit of measure for the device (syringe, medicine cup, etc.) that you are using to measure the dose. For example, if you are using a syringe calibrated in tenths of a milliliter, round to the nearest tenth of a milliliter. Rounding examples: To round to the nearest tenth of an mL: 1.53 rounds to 1.5 mL To round to the nearest hundredth: 16.699 rounds to 16.7 (in science class you would leave the trailing zero, 16.70, to indicate the level of precision; in medical use, omit trailing zeros to avoid error)
Scored tablets can be rounded to the nearest half tablet. 1.8 tablets would round to 2 tablets, 1.4 tablets would round to 1.5 tablets, and 1.2 tablets would round to 1 tablet. Check with a pharmacist to see if the pill is available in a dose strength that would be more accurate than rounding and breaking tablets.
III. Equivalents:
Volume: Metric Household Apothecary 5 mL = 1 teaspoon (tsp) = 1 teaspoon (tsp) 15 mL = 1 tablespoon (Tbsp) = 1 tablespoon (Tbsp) 30 mL = 2 tablespoons = 1 ounce 240 mL = 1 measuring cup = 8 ounces 500 mL = 1 pint = 16 ounces 1000 mL = 1 quart = 32 ounces
Weight: Metric Apothecary 1 kg = 2.2 lb 1 gm = 15 grains (gr xv) 60 mg = 1 grain (gr i) 0.6 mg = gr 1/ 0.4 mg = gr 1/ 0.3 mg = gr 1/
IV. Ratio and Proportion
A ratio can be expressed as a fraction; for example, the ratio 1:4 can be expressed as ¼ and 3:8 can be expressed as ⅜. Similarly, the ratio 5:1 would be written as 5/1.
When you are solving a drug calculation problem using the ratio & proportion method, you are always comparing what you know to what you do not know:
KNOWN UNKNOWN Amount of drug in the vehicle on hand = amount of drug ordered Vehicle on hand (cap, tab, mL) amount of vehicle needed for the ordered dose
For example, suppose the doctor orders 750 mg of Amoxicillin and you have a bottle of 250 mg capsules of Amoxicillin on hand. What you know is that there are 250 mg per (or in) one capsule. This can be set up as a ratio of 250 mg : 1 capsule or 250/1. What you do not know is how many capsules you will need to administer to the patient to give him 750 mg of the drug. So the unknown is 750 mg per an unknown number of capsules. An unknown quantity is expressed as “X” so the ratio becomes 750 mg : X capsules. To set up a proportion, you would write “ 250 : 1 :: 750 : X,” which is read “250 is to 1 as 750 is to X.” When the ratios are converted to fractions, you can write the proportion as an equation:
250mg = 750mg (where X represents the 1 cap X cap number of capsules needed to make the ordered dose)
You cross multiple and solve the equation for X: 250 x X = 1 x 750 or 250X = 750 if you divide both sides by 250, the equation simplifies to: X = 3 capsules
VI. IV Calculations A. Calculating Drip Rates Calculating the drip rate to manually regulate an IV requires two steps:
- Calculate the infusion rate of the IV in milliliters per hr (mL/hr) Divide the total volume to be infused by the number of hours over which it will infuse. For example: 1,000 mL to infuse over 8 hours 1,000 mL = 125 mL/hr 8 hr
- Calculate the drops per minute (gtt/min) needed to achieve this infusion rate To calculate the gtt/min from the mL/hr, you need to know the drop factor of the IV tubing you are using. This is the number of drops that are required to make one milliliter and it will vary depending on the tubing you are using; it could be 10, 15, 20, or 60—most blood tubing is 10 gtt/mL and all minidrip (or microdrip) tubing is 60 gtt/mL. The formula is: Infusion Amount (mL) x Drop factor (gtt/mL) = gtt/min Infusion time (min) (note: the infusion time may not always be one hour (60 minutes); see Example 2 below)
Example 1: The ordered infusion rate is 1L over 12 hours and the drop factor of the tubing is 15 gtt/mL. Step one: Calculate the hourly infusion rate 1,000 mL = 83.3 mL/hr or 83 mL/hr (same as 83 mL/60 min) 12 hr Step two: Calculate gtt/min (infusion amount = 83 mL, drop factor = 15, and infusion time = 60 min) 83 mL x 15gtt/mL = 20.75 gtt/min → 21 gtt/min 60 min For infusions that require less than an hour: Example 2: You are to infuse Ancef 1 gm in 100 mL NS every 12 hours. Your drug book says that this medication can be infused over 20 min. The drop factor of the tubing is 20. Step one: You do not need to calculate an infusion rate because it is already given, it will be 100 mL (infusion amount) over 20 min.(infusion time)
Step two: Calculate gtt/min 100 mL x 20 gtt/mL = 100 gtt/min 20 min
Short cut method: If you know the rate of the infusion in ml/hr and the drop factor of the tubing, then: Divide the infusion If the drop factor is: rate (mL/hr) by: 10 6 15 4 to get the infusion rate 20 3 in gtt/min. 60 1
For example 2 above, the infusion rate of the Ancef in mL/hr can be calculated using ratio proportion and would be 300mL/hr. With a drop factor of 20, you would divide the 300 by 3 to get a drip rate of 100 gtt/min.
B. Calculating Drug infusion rates by weight Order: 3mcg/kg/min of Intropin (dopamine HCl) for a new patient with heart failure. Available: 400 mg Intropin in 500 mL D 5 W. The patient’s weight is 242 pounds. What is the flow rate of the IV?
Step 1: Convert the patient’s weight to kilograms (because the order is in kg). Use the conversion factor from page one: 1 kg = 2.2 pounds 242 lb. = 110 kg or 1 kg = X kg → 2.2X = 242 (using ratio/ 2.2 lb/kg 2.2 lbs 242 lbs X = 110 kg proportion) Step 2: Calculate how much medication the patient should receive in an hour (because your infusion rate will be in mL/hr. 3 mcg x 110 kg x 60 min = 19,800 mcg/hr Because the drug on hand is in mg, convert this answer to mg → 19.8 mg/hr
Use ratio/proportion to find the infusion rate: 400 mg = 19.8 mg → 400X = 9900 X = 24.75 mL The infusion rate will be 500 mL X mL 25 mL/hr. Note that is a critical care unit, you may have infusion pumps that are capable of delivering infusion rates in tenths of a milliliter. In that situation, you would round your answer to the nearest 0.1 mL (24.8 mL) rather than to the nearest whole mL.
C. Calculating Heparin infusion rates Order: 1400 units/hr. Available: 25,000 units of Heparin in 500 mL NS What will the infusion rate of the Heparin solution be?
This can be solved by setting up a simple ratio/proportion problem 500 mL = X mL → 25,000 X = 700,000 The infusion rate will be 25,000 units 1400 units X = 28 mL 28mL/hr.
D. Formula method You can use the formula method to solve med calc problems as well. That formula is X = D x V Where X = the dose you will give (in terms of the vehicle) H D = the ordered dose H = the dose on hand V = the vehicle on hand To use this formula, make sure that D and H are in the same unit of measure V represents the vehicle (volume) of the drug on hand (1 capsule, 5 mL, etc.) Taking the problem from C above:
D = 1400 units/hr H = 25,000 units X = 1400u/hr x 500mL → X = 700,000 → X = 28 mL/hr V = 500 mL 25,000u 25,
