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.

CALCULATIONS

CHAPTER 6

ROMAN NUMERALS

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.

METRIC SYSTEM LIQUIDS

METRIC SYSTEM SOLIDS

AVOIRDUPOIS SYSTEM

APOTHECARY SYSTEM

HOUSEHOLD UNITS

TEMPERATURE

9C = 5F - 160For example, to convert 37C to Fahrenheit:

9(37) = 5(F) – 160333 = 5F – 160493 = 5F98.6 = F

For example, to convert 98.6F to Celsius:

9C = 5(98.6) – 1609C = 493 – 1609C = 333C = 37

RATIO & PROPORTION

• A ratio states a relationship between two quantities

• Two equal ratios form a proportion

Rules for using ratios and proportions

1. 3 of the 4 values must be known2. Numerators (values in front of colons) must have same units3. Denominators (values behind colons) must have same units

ExamplesYou receive a prescription for KTabs one tablet bid x 30 days. How many tablets are needed to fill this prescription?

1. Define the variable and correct rations:

Unknown variable (X) is the total tablets neededKnown ratio is 2 tablets per dayUnknown 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

ExamplesIf 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:1.2ml2.8ml3.75ml4.2.08 ml/mn5.4.8 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 ExamplesIf 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)

1. 60%2. 80%3. 12%4. .55. .1256. .997. 35g8. 52.5g9. 14g10.50ml11.70ml12.20ml13.0.12%

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 highest strength

component in the lower left hand

box.

Place the desired strength in the

middle box.

POWDER VOLUME

FV = D + PV

Final volume = Diluent + Powder volume

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 mL2 – 5 mL 2 – 0.5 mL3 – 10 mL 3 – 0.5 mL

Example

FV = D+PV or D = FV – PV

1 - D = 2mL – 0.5mL = 1.5 mL2 - D = 5 mL – 0.5 mL = 4.5 mL3 - 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 13 What is the powder volume?

Step 1. Calculate the final volume. The strength of the final solution will be 100 mg/mL.

Example What is the powder volume?

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

• Clark’s Rule

• Young’s Rule

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

Uses Weight in Lbs, NEVER in Kg.

Here is the formula:

Adult Dose X (Weight ÷ 150) = Childs Dose

Example11 year old girl / 70 Lbs

500mg X (70 ÷ 150) = Child's Dose

500mg X ( .47 )= Child's Dose

500mg X .47 = 235mg

Child's Dose = 235Mg

Young's RuleYoung’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 Dose

Example11 year old girl / 70 Lbs

500mg X (11 ÷ (11+12)) = Child's Dose

500mg X (11 ÷ 23) = Child's Dose

500mg X .48 = Child's Dose

Child's Dose = 240mg

CALCULATIONS FOR BUSINESSAverage 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