To find out how many milliliters (mL) of the drug to administer, we need to convert the dosage and use a proportion to calculate the correct amount.

Step 1: Convert 0.8 mg to micrograms (mcg)

Since 1 mg = 1,000 mcg, we multiply: $0.8 \, \text{mg} = 0.8 \times 1,000 = 800 \, \text{mcg}$

Step 2: Set up a proportion

The drug is supplied at 900 mcg per 5 mL. We need to find how many milliliters contain 800 mcg.

Using the proportion: $\frac{900 \, \text{mcg}}{5 \, \text{mL}} = \frac{800 \, \text{mcg}}{x \, \text{mL}}$

Step 3: Solve for $x$

Cross-multiply to solve for $x$: $900 \times x = 800 \times 5$ $900x = 4000$ $x = \frac{4000}{900} = 4.44 \, \text{mL}$

Conclusion:

You should administer 4.44 mL using the 5 mL syringe.

Would you like further clarification on any step?

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Here are 5 related questions for you to consider:

1. How would the calculation change if the dosage was in milligrams directly?
2. What happens if the drug is supplied in a different concentration, such as 600 mcg per 5 mL?
3. How can rounding rules affect medication administration in this case?
4. Why is it important to convert between units when calculating dosages?
5. How do you ensure the syringe measurement is accurate?

Tip: Always double-check the concentration of the drug and the patient's weight if applicable to ensure the correct dose is administered!