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# Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

## Parenteral Medications

Parenteral medications are those that are injected into the body by various routes. Drugs for parenteral medications may be packaged in various forms such as ampules, vials, and prefilled cartridges or syringes.

Examples:

1. A physician orders octreotide acetate 50 mcg s.c. q.8.h. Using the label, determine how many milliliters of this hormone suppressant you will administer. Indicate the dose on the syringe shown.

We have to convert 50 mcg into millilitres given that the label reads 200 micrograms per 1 millilitre.

$50\,mcg\times\frac{1\,mL}{200\,mcg}=0.25\,mL$

0.25 mL of octreotide acetate would be administered subcutaneously every eight hours.

2. An order is placed for penicillin G potassium 200,000 units IM stat q.6.h.

a. Calculate the number of millilitres of this antibiotic you would administer to the patient if you use the 18.2 mL of diluent to reconstitute the drug.

On the right side of the label there are four options: 250,000 units/mL; 500,000 units/mL; 750,000 units/mL; 1,000,000 units/mL

Since the order is close to 250,000 units/mL, we will choose the first option 18.2 mL of diluent to be added to obtain a dosage strength of 250,000 units/mL.

Inject 18.2 mL of air into a vial of sterile water for injection and then withdraw 18.2 mL of sterile water. Add the sterile water to the penicillin G potassium vial and shake well. Now the vial contains a solution which $$1\,mL=250,000\,units$$.

Now, we need to convert 200,000 units into mL.

$200,000\,units\times\frac{1\,mL}{250,000\,units}=\frac{20\,mL}{25}=0.8mL$

You would withdraw 0.8 mL from the vial and administer it to the patient immediately then every six hours.

b. Which syringe is the most appropriate to use to withdraw from the vial and administer to the patient?

Answer is the second one because we can accurately measure 0.8 mL.

3. A physician orders Fragmin (dalterparin sodium) 120 units/kg S.C. q.12.h. for a patient who weighs 138 pounds. How many millilitres of this low molecular weight heparin will you need to administer?

Important information:

• patient is 138 lb
• order is 120 units/kg
• strength of drug on label is 5000 units/0.2 mL
• we need to find the dosage in mL to administer

Since the order is per kg, but the patient's weight is in pounds. We need to convert the weight into kg (1 kg = 2.2. lb).

$138\,lb\times\frac{1\,kg}{2.2\,lb}=62.727272727\,kg$

Now, we find the units based on the order of 120 units/kg

$62.727272727\,kg\times\frac{120\,units}{kg}=7.527272727\,units$

Finally, we use the strength of the drug 5000 units/0.2 mL to find the dosage.

$7.527272727\,units\times\frac{0.2\,mL}{5000\,units}=0.301mL$

Therefore, you would administer 0.3 mL of Fragmin subcutaneously every 12 hours.