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# Pharmacy calculations

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### Pharmacy calculations

1. 1. Pharmacy Calculations Numbers/Fractions Decimal/Significant Figures Measurements/Equations & Variables Ratio & Proportion Percents & Solutions
2. 3. Numerals <ul><li>ss </li></ul><ul><li>I or i </li></ul><ul><li>V or v </li></ul><ul><li>X or x </li></ul><ul><li>L or l </li></ul><ul><li>C or c </li></ul><ul><li>D or d </li></ul><ul><li>M or m </li></ul><ul><li>ROMAN </li></ul><ul><li>0.5 or ½ </li></ul><ul><li>1 (one) </li></ul><ul><li>5 </li></ul><ul><li>10 </li></ul><ul><li>50 </li></ul><ul><li>100 </li></ul><ul><li>500 </li></ul><ul><li>1000 </li></ul><ul><li>ARABIC </li></ul>
3. 4. Practice Problems <ul><li>Caps no. xiv </li></ul><ul><li>Gtts ix </li></ul><ul><li>Tabs # XLVIII </li></ul><ul><li>Tabs # xxi </li></ul><ul><li>Gms xlv </li></ul><ul><li>ii tsps </li></ul><ul><li>Positional Notation--- </li></ul><ul><li>Position of the number carries a mathematical significance or value- </li></ul><ul><li>14 capsules </li></ul><ul><li>9 drops </li></ul><ul><li>48 tablets </li></ul><ul><li>21 tablets </li></ul><ul><li>45 grams </li></ul><ul><li>2 teaspoonfuls </li></ul><ul><li>Second of two letters is: </li></ul><ul><li>Smaller --- ADD </li></ul><ul><li>Larger --- SUBTRACT </li></ul>
4. 5. A Fraction…… <ul><li>Is a numerical representation indicating there is a part of a whole (3/4,5/8). </li></ul><ul><li>Represents the division of two numbers. </li></ul><ul><li>Has a denominator (number below the bar), which tells us how many parts the whole is divided into. </li></ul><ul><li>Has a numerator (number above the bar), which tells us how many of those parts exist. </li></ul><ul><li>One way to think of a fraction is as a division that has not been completed. </li></ul><ul><li>¼ 0.25 25/100 25% </li></ul><ul><li>½ 0.5 50/100 50% </li></ul><ul><li>¾ 0.75 75/100 75% </li></ul>
5. 6. Decimal Numbers Power of 10 <ul><li>Adding & Subtracting </li></ul><ul><li>First- put the #’s in a vertical column </li></ul><ul><li>Aligning decimal points </li></ul><ul><li>Add starting Right to Left and carry </li></ul><ul><li>Subtract starting Rt-Lt and borrow </li></ul><ul><li>4 + 3.1 + 0.3 + 5.001= ? </li></ul><ul><li>4.0 </li></ul><ul><li>3.1 </li></ul><ul><li>0.3 </li></ul><ul><li>5.001 = 12.401 </li></ul><ul><li>Subtract 1.203 from 32.55 </li></ul><ul><li>32.55 </li></ul><ul><li>- 1.203 = 31.347 </li></ul>
6. 7. Decimals cont. <ul><li>Multiplying Decimals </li></ul><ul><li>First, align numbers on the right </li></ul><ul><li>Multiply normally & add the products </li></ul><ul><li>Finally, count the decimal places </li></ul><ul><li>Multiply 9.683 by 6.1 </li></ul><ul><li>9.683 </li></ul><ul><li>x 6.1 </li></ul><ul><li>9683 </li></ul><ul><li>58098 </li></ul><ul><li>590663 how many decimals? </li></ul><ul><li>59.0663 </li></ul>
7. 8. Significant Figures <ul><li>The actual value we can use in our calculations depends on the sensitivity of the measuring device. Last figure to the right is approximation. RULES </li></ul><ul><ul><li>Digits other than zero are always significant 453.7g </li></ul></ul><ul><ul><li>Final zeros after a decimal point are always significant 0.100mg=100mcg </li></ul></ul><ul><ul><li>Zeros between two other significant digits are always significant 101g </li></ul></ul><ul><ul><li>Zeros used only to show the location of the decimal are never significant 0.123mg 00123.4560 </li></ul></ul><ul><li>Rounding off retains significance of least # </li></ul><ul><ul><ul><li>1.65370 x 0.26 = 1.65 x 0.26 = 0.4290 = 0.43 </li></ul></ul></ul>
8. 9. Pharmacy Measurement Systems <ul><li>Metric System </li></ul><ul><ul><li>Liquids (Volume) </li></ul></ul><ul><ul><ul><li>Liter 1L = 10 dL = 1000mL </li></ul></ul></ul><ul><ul><ul><li>Milliliter 1mL = 0.001 L </li></ul></ul></ul><ul><ul><ul><ul><li>Milliliters = cubic centimeters (cc) </li></ul></ul></ul></ul><ul><ul><li>Solids (Weight) </li></ul></ul><ul><ul><ul><li>Kilogram 1kg = 1000g </li></ul></ul></ul><ul><ul><ul><li>Gram 1g (gm) = 0.001kg=1000mG </li></ul></ul></ul><ul><ul><ul><li>Milligram 1mG= 0.001g=1000mcg </li></ul></ul></ul><ul><ul><ul><li>Microgram 1 mcg= 0.001mG =0.000001g </li></ul></ul></ul><ul><ul><li>Length (na) </li></ul></ul>
9. 10. Measurements cont. <ul><li>Avoirdupois System </li></ul><ul><ul><li>Pound 1 lb=16oz </li></ul></ul><ul><ul><li>Ounce 1 oz=437.5 </li></ul></ul><ul><ul><li>Grain 1gr=64.8mg </li></ul></ul><ul><li>Apothecary System (Metric) </li></ul><ul><ul><li>Gallon 1gal=4qt 3840mL </li></ul></ul><ul><ul><li>Quart 1qt=2pt 960mL </li></ul></ul><ul><ul><li>Pint 1pt=16 fl oz 480mL </li></ul></ul><ul><ul><li>Fluid Ounce 1fl oz=6 fl dr 30mL </li></ul></ul><ul><ul><li>Fluid dram 60 minims 5 mL </li></ul></ul>
10. 11. Measurements cont. <ul><li>Household units </li></ul><ul><ul><li>Teaspoon 1 tsp=5mL </li></ul></ul><ul><ul><li>Tablespoon 1tbsp=3tsp=15mL </li></ul></ul><ul><ul><ul><li>2 tbsp = 30ml = 1 fl oz </li></ul></ul></ul><ul><ul><li>Cup 1cup=8 fl oz </li></ul></ul><ul><li>Temperature ~~~ </li></ul><ul><ul><li>Centigrade (Celsius) C </li></ul></ul><ul><ul><li>Fahrenheit, F </li></ul></ul><ul><ul><ul><li>9C=5F-160 </li></ul></ul></ul><ul><li>International Units </li></ul><ul><ul><li>IU </li></ul></ul><ul><ul><li>Measures the amount of drug in units </li></ul></ul><ul><ul><li>Penicillin, heparin, insulin, vitamin E </li></ul></ul><ul><li>Milliequivalents </li></ul><ul><ul><li>mEq </li></ul></ul><ul><ul><li>Refer to positively charged ions per liter of salt solution </li></ul></ul><ul><ul><li>Klor-con 8mEq </li></ul></ul>
11. 12. Conversions <ul><li>Change one unit of measure into another </li></ul><ul><li>1pt=473.167mL (473mL) (480mL) </li></ul><ul><li>1 fl oz=29.57mL (30mL) </li></ul><ul><li>1kg=2.2lb </li></ul><ul><li>1g=1000mG </li></ul><ul><li>1lb=453.59gm (454g) </li></ul><ul><li>1oz=28.35gm (30g) </li></ul><ul><li>1gr=64.8mG (65mg) </li></ul><ul><li>1g=1000mG </li></ul><ul><li>1 fl dr= 5mL </li></ul>
12. 13. Equations & Variables X <ul><li>An equation is a mathematical statement in which two terms are equal. </li></ul><ul><li>There is often an unknown value that needs to be determined, called a variable, indicated by x. </li></ul>
13. 14. Problem Solving an RX <ul><li>RX: Amoxicillin 250mg tid for 7 days. How many capsules need to be dispensed? </li></ul><ul><li>(doses needed) x =(caps per dose)(dose/day) (days) </li></ul><ul><li>x=1x3x7 = 21 capsules of Amoxicillin to fill the Rx. </li></ul><ul><li>RX: Phenergan w/Cod Liq 120 ml How many Fluid ounces will be dispensed? </li></ul><ul><li>x fl oz= (total prescribed ml) x (conversion Rate) </li></ul><ul><li>x fl oz= 120 ml x 1 fl oz </li></ul><ul><li>29.57 ml </li></ul><ul><li>x fl oz = 4 (approx) </li></ul>
14. 15. Ratio and Proportion~ <ul><li>A relationship between two quantities : A or A:B </li></ul><ul><li>B </li></ul><ul><li>RULES for Solving </li></ul><ul><li>Three of the four values must be known </li></ul><ul><li>Numerators must have the same units </li></ul><ul><li>Denominators must have the same units </li></ul><ul><li>Two equal ratios form a proportion : </li></ul><ul><li>A = C or AD=BC </li></ul><ul><li>B D </li></ul><ul><li>STEPS for Solving~~ </li></ul><ul><li>Write problem in ratio form </li></ul><ul><li>Select conversion equation </li></ul><ul><li>Diagonal multiply & divide </li></ul><ul><li>OR </li></ul><ul><li>x=( D esired) x Q uantity~~ </li></ul><ul><li>H ave </li></ul>
15. 16. Critical Thinking ERRORS ! <ul><li>RX Prelone 15mG /5mL </li></ul><ul><li>15mG po BID </li></ul><ul><li>ERROR: Order misread 15mL BID </li></ul><ul><li>Patient received 15 mL instead of 5 mL or 45 mG </li></ul><ul><li>Potential Outcome: hi dose steroid </li></ul><ul><li>GI bleed, HA, Seizures, HTN </li></ul><ul><li>PREVENTION: </li></ul><ul><li>mG is weight – mL is volume </li></ul><ul><li>RX ASA 325mg </li></ul><ul><li>10gr qd </li></ul><ul><li>ERROR: Order misread </li></ul><ul><li>10 grams </li></ul><ul><li>Patient received 16 times dose </li></ul><ul><li>Potential Outcome: GI heartburn,nausea,bleed </li></ul><ul><li>PREVENTION: order in apothecary, supply in metric,decimal point </li></ul><ul><li>10gr (60mg/1gr)=600mg </li></ul>
16. 17. Percents and Solutions <ul><li>Are used to indicate the amount or concentration of something in solution </li></ul><ul><li>Concentrations are in terms of weight to volume OR volume to volume </li></ul><ul><li>Wt per Vol (w/v) = grams per 100 milliliters g/100mL </li></ul><ul><li>Vol per Vol (v/v) =milliliters per 100 millilters ml/ 100mL </li></ul><ul><li>Wt per Wt (w/w) = grams per 100 grams g/100 g </li></ul>Part Whole %
17. 18. Critical Thinking ERRORS ! <ul><li>RX Keflex 80mg po QID </li></ul><ul><li>Supply Keflex 250mg/5ml </li></ul><ul><li>ERROR Incorrect ratio setup </li></ul><ul><li>Patient received 9.75 x dose </li></ul><ul><li>80mg = 250 mg x=15.6ml </li></ul><ul><li>5 ml x ml </li></ul><ul><li>Potential Outcome :renal/liver </li></ul><ul><li>Impairment; BUN/liver labs; </li></ul><ul><li>Family notified & incident report </li></ul><ul><li>PREVENTION: correct ratio </li></ul><ul><li>250mg = 80 mg x=1.6ml </li></ul><ul><li>5ml x ml </li></ul><ul><li>Desired x Q = x </li></ul><ul><li>Have </li></ul><ul><li>80mg x 5ml = x </li></ul><ul><li>250mg </li></ul><ul><li>*check that units cancel </li></ul><ul><li>*check that number makes sense </li></ul>
18. 19. Practice Pharmacy Problems