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## CALCULATIONS

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**CALCULATIONS**CHAPTER 6**ROMAN NUMERALS**• Positional notation • When the second of two letters has a value equal to or smaller than that of the first, add their values • ixvi = 50 + 10 + 5 + 1 = 66 • When the second of two letters has a value greater than that of the first, subtract the smaller from the larger • xc = 10 subtracted from 100**SIGNIFICANT FIGURES**• Four rules for assigning significant figures: 1. Digits other than zero are always significant. 2. Final zeros after a decimal point are always significant. 3. Zeros between two other significant digits are always significant. 4. Zeros used only to space the decimal are never significant.**TEMPERATURE**9C = 5F - 160 For example, to convert 98.6F to Celsius: 9C = 5(98.6) – 160 9C = 493 – 160 9C = 333 C = 37 For example, to convert 37C to Fahrenheit: 9(37) = 5(F) – 160 333 = 5F – 160 493 = 5F 98.6 = F**RATIO & PROPORTION**Rules for using ratios and proportions 3 of the 4 values must be known Numerators (values in front of colons) must have same units Denominators (values behind colons) must have same units A ratio states a relationship between two quantities Two equal ratios form a proportion**Examples**You receive a prescription for KTabs one tablet bid x 30 days. How many tablets are needed to fill this prescription? Define the variable and correct rations: Unknown variable (X) is the total tablets needed Known ratio is 2 tablets per day Unknown ratio is how many tables are needed for 30 days 2. Set up the proportion equation: X tabs : 30 days = 2 tabs : 1 day 3. Solve: X = 60 tabs**Examples**If an antidiarrheal mixture contains 3ml of paregoric in each 30ml of mixture, how many ml of paregoric would be contained in a tsp of mixture? (note 1 tsp = 5ml) 3ml paregoric : 30ml mixture = xml paregoric : 5ml mixture 15ml = 30x 0.5ml = x**Complete page 143 1-5:**Answers: 2ml 8ml 75ml 2.08 ml/mn 4.8 ml**Percents & Solutions**Percents are used to indicate the amount, or concentration, of something in a solution. Weight-to-Volume: grams per 100 milliliters g/100ml Volume-to-Volume: milliliters per 100 milliliters ml/100ml**PERCENTS & SOLUTIONS**• Percent Weight-to-Volume • Grams per 100 milliliters • Percent Volume-to-Volume • Milliliters per 100 milliliters • Milliequivalents • mEq**Percents / Solutions Examples**If there is 50% dextrose in a 1,000 ml IV bag, how many grams of dextrose are there in the bag? 1. Proportion equation: Since 50% dextrose means there are 50 grams of dextrose in 100 ml, the equation would be: xg / 1,000ml = 50g / 100ml 2. The x equation: xg = 1,000ml x 50g/100ml = 10 x 50g = 500g Answer = There are 500g of dextrose in the bag**Example**Now how many ml will give you a 10g of dextrose solution? 1. The proportion equation: xml: 10g = 100ml: 500g 2. The x equation: 500xml/g = 1000ml/g X = 20ml**Complete page 145 1-13 (click for answers)**60% 80% 12% .5 .125 .99 35g 52.5g 14g 50ml 70ml 20ml 0.12%**ALLIGATION**A way to solve problems when mixing preparations of 2 different strengths of the same ingredient to obtain a strength in-between the starting preparation. Use a tic-tac-toe grid. Place the lowest strength component in the upper left hand box. Place the highest strength component in the lower left hand box. Place the desired strength in the middle box. Place the lowest strength component in the upper left hand box. Place the desired strength in the middle box. Place the higheststrength component in the lower left hand box.**POWDER VOLUME**FV = D + PV Final volume = Diluent+ Powder volume**Example**A dry powder antibiotic must be reconstituted for use. The label states that the dry powder occupies 0.5 mL . Using the formula for solving powder volume, determine the diluent volume (the amount of solvent added). You are given the final volume for three different examples with the same powder volumes. Final Volume Powder Volume 1 – 2 mL 1 – 0.5 mL 2 – 5 mL 2 – 0.5 mL 3 – 10 mL 3 – 0.5 mL**FV = D+PV or D = FV – PV**1 - D = 2mL – 0.5mL = 1.5 mL 2 - D = 5 mL – 0.5 mL = 4.5 mL 3 - D = 10 mL – 0.5 mL = 9.5 mL**Example**You are to reconstitute 1 g of dry powder. The label states that you are to add 9.3 mL of diluent to make a final solution of 100 mg/mL. What is the powder volume?**Example 13What is the powder volume?**Step 1. Calculate the final volume. The strength of the final solution will be 100 mg/mL.**Example**Dexamethasone is available as a 4 mg/mL preparation. An infant is to receive 0.35 mg. Prepare a dilution so that the final concentration is 1 mg/mL. How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire vial?**Example How much diluent will you need if the original**product is in a 1 mL vial and you dilute the entire vial?**Example How much diluent will you need if the original**product is in a 1 mL vial and you dilute the entire vial?**CHILDREN’S DOSES**These methods are used when either the manufacturer has not recommended dosages for children or the prescriber has requested them to be used. The best explanation for these is simply that children vary so much in weight, size, tolerances, etc. Clark’s Rule Young’s Rule**Clark's Rule**Uses Weight in Lbs, NEVER in Kg.Here is the formula:Adult Dose X (Weight ÷ 150) = Childs DoseExample11 year old girl / 70 Lbs500mg X (70 ÷ 150) = Child's Dose500mg X ( .47 )= Child's Dose500mg X .47 = 235mgChild's Dose = 235Mg**Young's Rule**Young’s Rule uses age.(which makes it easier to remember, the word young refers to age)Here is the formula:Adult Dose X (Age ÷ (Age+12)) = Child's DoseExample11 year old girl / 70 Lbs500mg X (11 ÷ (11+12)) = Child's Dose500mg X (11 ÷ 23) = Child's Dose500mg X .48 = Child's DoseChild's Dose = 240mg**CALCULATIONS FOR BUSINESS**Average wholesale price (AWP) + professional fee = selling price of prescription Gross profit = difference between the selling price and the cost of acquiring the product (acquisition cost) Net profit = difference between the selling price and all the costs associated with filling the prescription (dispensing fee) Gross profit = selling price – acquisition cost Net profit = gross profit – dispensing fee