CALCULATIONS CHAPTER 6. ROMAN NUMERALS Positional notation – When the second of two letters has a...
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Transcript of CALCULATIONS CHAPTER 6. ROMAN NUMERALS Positional notation – When the second of two letters has a...
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 - 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
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.
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
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