Calculations Review

Calculations Review

Metric System

• Kilo- 1000 times- a measure of weight -1 kg = 1000 grams• Deci - 0.01 - one tenth• Centi - 0.01 (one hundredth part of) - • Milli - 0.001 - one thousandth part of• Micro - 0.000001 - one millionth part of

• Gram is used to measure weight • Liter is used to measure fluid• Meter is used to measure length

• Gram = g• Microgram = mcg• Milligram = mg• Kilogram = kg• Liter = L• Deciliter = dl• Milliliter = mL

Rules

• Always place a leading zero to the left of the decimal point if there is no whole number. Eliminate trailing zeros to the right of the decimal point.

• Do not use the abbreviation cc for ml (2 ml; not 2 cc).

• Use a full space between the numeral and the abbreviation (2 mL; not 2mL).

Metric Equivalents to Memorize

• Weight:– 1 kilogram (kg) = 1,000 grams (g)– 1 gram (g) = 1,000 milligrams (mg)– 1 milligram (mg) = 1,000 micrograms (mcg)


• Volume:– 1 liter (L) = 1,000 milliliters (mL)– 1 milliliter (mL) = 0.001 liter (L)


• Length:– 1 meter(m)=100 centimeters(cm)=1000mm– 1 millimeter (mm) = 0.002 meter(m)=0.1cm

Practice Conversion Problems

• 1. 300 mg = _____ g

• 2. 6 mg = ______mcg

• 3. 0.7 L = _____mL

• 4. 180 mcg = ____mg

• 5. 0.02 mg = _____ mcg

• 6. 4.5 L = ____mL

• 7. 4.2 g = _____mg

• 8. 0.9 g = ____ mg

• 9. 3,250 ml = ____L

• 10. 42 g = _____ kg

• 11. 529 mg = ____ g

• 12. 645 mcg = _____ mg

• 13. 347 L = ______ mL

• 14. 238 g = _____mcg

• 15. 3,500 mL = _____L

Answers to Practice Problems• 1. 0.3 g• 2. 6,000 mcg• 3. 700 mL• 4. 0.18 mg• 5. 20 mcg• 6. 4,500 mL• 7. 4,200 mg• 8. 900 mg• 9. 3.25 L• 10. 0.042 kg• 11. 0.529 g• 12. 0.645 mg• 13. 347,000 mL• 14. 238,000,000 mcg• 15. 3.5 L

Apothecary System

• 1 ounce (oz) = 30 mL (double-headed z symbol)• 1 tablespoon (T or tbs) = 15 mL• 2 tablespoons (T or tbs) = 1 ounce (oz)• 1 teaspoon (t or tsp) = 5 mL• 1 cup = 240 mL (8 ounces)• 1 pint (pt) = 500 mL (16 ounces)• 1 quart (qt) = 1,000 mL (32 ounces)

• 15 grains (gr) = 1,000 mg = 1 gram (g)• 1 grain (gr) = 60 mg• 1 pound (lb) = 16 ounces (oz)• (use clock analogy to remember grains (gr). 60 minutes = 1 hour, 60 mg = gr 1.

30 mg = gr 1/2. 15 mg = gr 1/4, 45 mg = gr 3/4.)• 2.2 lb = 1 kg (1,000 g)

Apothecary System Practice Problems

• 1. oz 1/2 = _____mL

• 2. 2 tsp = _____mL

• 3. 45 mL = ____tbs

• 4. 1/2 pt = oz____

• 5. 90 ml = oz____

Answers to Apothecary Practice Problems

• 1. 15 mL

• 2. 10 mL

• 3. 3 tbs

• 4. oz 8

• 5. oz 3

Converting

• You have to memorize the equivalents!

• Practice Problems:• 600 ml =____L• 0.016 g = _____mg• 4 kg = ____ g• 3 mcg = ____ mg• 0.3 mg = ____ g• 0.01 kg = ____ g• 1.9 L = ____ mL• 0.5 g = _____ kg• 0.07 mg = ____ mcg

Answers to Converting Problems

• 0.6 L• 16 mg• 4,000 g• 0.003 mg• 0.0003 g• 10 g• 1,900 mL• 0.0005 kg• 70 mcg

Ratio and Proportion

• Rules for Ration and Proportion– State the known equivalent first (memorized equivalent).– Add the incomplete ration on the other side of the equals sign, making sure

that the units of measurement are written in the same sequence. (mg:g = mg:g).

– Label all terms in the proportion, including “x”.– Solve the problem by using the principles for solving ratios and proportions. – The final answer for “x” should be labeled with the appropriate unite of

measure or desired unit. – Remember that the terms must correspond with each other in value. – Example: 8 mg = ____ g

• 1000 mg : 1 g = 8 mg : x g

• (the product of the means equals the product of the extremes)

• 1000 x = 1 times 8; 8/1000 = 0.008 g

Dimensional Analysis

• Steps:– Identify the unit you are converting to.– Write the conversion factor so that the desired unit

is in the denominator, and write the unit in the successive numerator to match the previous unit of measure in the previous denominator.

– Cancel the alternate denominator/numerator units to leave the unit desired (being calculated).

– Perform the mathematic process indicated.

Converting between systems

Involves a multi step process. You have to memorize the equivalents!

Example 1: Gr 1/100 = ____ mgEquivalent: gr 1 = 60 mgDivide 60/100. Answer 0.6 mg

Example 2:110 lb = ____ kgEquivalent: 1 kg = 2.2 lb110/2.2 = 50 kg

Example 3:Gr 1/10 = ____ mgEquivalent: gr 1 = 60 mg60/10 = 6 mg

Converting-Practice Problems

• 60 lb = ___ kg• 15 mg = gr ___• oz 5 = ____mL• gr v = ____ mg• 7 oz = ____ mL• 250 ml = ____ qt• 45 ml = ____ tbs• gr 45 = ____g• gr 1.5 = ____ mg• 20 mL = ___tsp

Answers: converting practice problems

• 1. 27.27 kg• 2. Gr 1/4• 3. 150 mL• 4. 300 mg• 5. 210 mL• 6. 1/4 qt• 7. 3 tbs• 8. 3 g• 9. 90 mg• 10. 4 tsp

Practice Word Problems 1

• 1. A client received 1,750 mL of IV fluid. How many liters of IV fluid did the client receive?

• 2. A client has an order for 125 mcg of digoxin. How many milligrams will you administer to the client?

• 3. A client has an order for 1,500 mL of water by mouth every 24 hours. How many ounces is this?

Answers to Practice Word Problems (1)

• 1. 1.75 L

• 2. 0.125 mg

• 3. 50 oz

Conversion between Celsius and Fahrenheit

• To covert from Celsius to Fahrenheit multiply by 1.8 and add 32

• Convert 37.5 C to F– 1.8 (37.5) + 32 = 99.5– To convert from Fahrenheit to Celsius,

subtract 32 and divide by 1.8– Covert 68 F to C– 68-32/1.8= C = 20

Conversions Relating to Length

• 1 cm = 10 mm

• 1 in = 2.54 cm

• Example: 30 cm/ 2.5 = 12 inches

Converting Pounds to Kilograms

• 2.2 lb = 1 kg

• Example: A child weighs 65 lb. Convert to kg.

• 65/2.2 = 29.5 kg

• Example 2: A child weighs 10 lb, 2 oz. Convert to kg

• 16 oz = 1 lb., 2 oz/16 = 0.12 = 0.1 lb

• 10 lb + 0.1 lb = 10.1 lb

• 10.1/ 2.2 = 4.59 = 4.6 kg

Converting to Kg. Practice Problems

• Covert the following to kg (rounding to nearest tenth):

• 1. 6 lb, 5 oz

• 2. 12 lb, 2 oz

• 3. 10 lb, 4 oz

• 4. 7 lb, 12 oz

• 5. 20 lb.

Answers to practice question (convert to Kg)

• 1. 2.9 kg

• 2. 5.5 kg

• 3. 4.7 kg

• 4. 3.5 kg

• 5. 9.1 kh

Converting Kilograms to Pounds

• To convert kilograms to pounds, multiply by 2.2. Answer is expressed to the nearest tenth.

• Example 1:

• A child weight 24.7 kg. Convert to pounds. 24.7 x 2.2 = 54.35 = 54.3 lb

Practice problems converting kilograms to pounds

• 1. 46 kg

• 2. 98.2 kg

• 3. 10.4 kg

• 4. 34.9 kg

• 5. 5.8 kg

Answers to practice problems converting kg to lb

• 1. 101.2 lb

• 2. 216 lb

• 3. 22.9 lb

• 4. 76.8 lb

• 5. 12.8 lb

Example questions for Dosage and Calculations

• 1. Order: 40 mg p.o. of a medication. Available: 20 mg tablets. How many tablets will you administer?

• 20/1 = 40/x. 40/20 = 2• 2. Order: 1 g p.o. of an antibiotic. Available:

500 mg capsules. How many capsules will you administer? Change mg to g. 500/1cap = 1000 mg/x. Answer 2 caps

Practice Problems

• Indicate whether you needs less than or more than one tablet:• 1. A client is to receive gr 1/300 of a medication. The tablets available are gr

1/150. How many tablets do you need? • 2. A client is to receive 1.25 mg of a medication. The tablets available are 0.652

mg. How many tablets do you need?• 3. A client is to receive gr 1/8 of a medication. The tablets available are gr 1/4.

How many tablets do you need?• Express the following answers in mL to the nearest tenth:• 4. Order: 7.5 mg p.o. Available: tablets labeled 5 mg.• 5. Order: gr 3/4 p.o. Available: Tablets labeled 30 mg. • 6. Order: 0.25 mg IM. Available: 0.5 mg per mL.• 7. Order: 100 mg p.o. of a liquid. Available: 125 mg per 5 mL. • 8. Order: 20 mEq IV . Available 40 mEq per 10 mL.

Answers to Practice Problems

• 1. Less than one tablet• 2. More than one tablet• 3. Less than one tab• 4. 1.5 tabs• 5. 1.5 tabs• 6. 0.5 mL• 7. 4 mL• 8. 5 mL

Intravenous Calculations

• IV fluids are usually ordered in mL/hr, unless administered without an infusion device at which time they are administered in drops per minute (gtt/min).

• Remember that the pump delivers volume in ml/hr, so if a decimal fraction is obtained, it must be rounded to the nearest whole number).

Examples

• 1. Client with an infusion pump has an order for 3,000 mL D5W over 24 hours. Calculate the infusion rate. 3000/24 = 125 ml/hr

• 2. A client with an infusion pump is to receive an antibiotic in 50 mL of 0.9% NS over 30 minutes. Calculate the infusion rate. 50:30 = x:60. The pump must be set to infuse 100 mL/hr for 50 mL to infuse within 30 minutes.

Calculationg IV Flow Rates in gtt/min

• IV tubing has a drop chamber. The nurse adjusts the clamp and observes the drop chamber to count the drops per minute.

• Two common types of tubing are used; Macrodrop Tubing and Microdrop Tubing.

• Macrodrop Tubing (standard): Delivers 10, 15 or 20 gtt equal to 1 mL.

• Microdrop Tubing (tiny drops): used in pedi and in critical care. Deliver 60 gtt equal to 1 mL. The number of microdrops per minute is equal to the number of mL/hr. For example, if clients are receiving 100 mL/hr, they are receiving 100 microdrops/min.

Calculating IV flow rates

• To calculate the flow rate, you must know 1) the volume or number of milliliters to infuse, 2) the drop factor (gtt/mL) of the IV tubing, and 3) the time element (minutes or hours).

• Formula: xgtt/min = (Amount of solution (mL) X Drop factor)/ Time

• Remember, drops are always expressed in whole numbers.

Example Calculating Drop Factor

• Order: D5W to infuse at 100 mL/hr. Drop factor 10 gtt/mL. At what rate in gtt/min should the IV be regulated?

• (x)gtt/min = (100 mL X 10 gtt/mL)/ 60 min.

• x = 17 gtt/min

Practice Drop Factor Problems

• 1. Administer D5LR at 75 mL/hr. The drop factor is 10 gtt/mL.

• 2. Administer D5 1/2 at 30 mL/hr. the drop factor is a microdrop.

• 3. Administer RL at 125 mL/hr. The drop factor is 15 gtt/mL.

• 4. Administer 1,000 mL D5 0.33% NS in 6 hr. The drop factor is 15 gtt/mL.

Answer to Drop Factor practice problems

• 1. 75x10/60 = 12.5 = 13 gtt/min

• 2. 30x60/60 = 30 gtt/min

• 3. 125x15/60 = 31.2 = 31 gtt/min

• 4. Calculate mL/hr. 1000 mL/6 hr = 167 mL/hr. Then calculate gtt/min. 167x15/60 = 41.7 or 42 gtt/min.

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Calculations Review