If dioxin 0.6 mg slow IV push stat is ordered and dioxin 500 mcg per 2 ml is available how many milliliters must be administered for the correct dose

Write all of the information from the question into an equation of all fractions. The fractions help us cancel out units that don't match our final answer.

When multiplying fractions, units that appear in both the numerator and denominator can be cancelled out.

Equation

Let's note on the left side that our final answer will be in millilitres. This means that the final answer units must only have mL in the numerator.

On the right side, we write out pieces of information from the question as separate fractions to be multiplied. We will also write in the conversion factor 1000 mcg per 1 mg.

[tex]mL\ to\ administer=\dfrac{0.6\ mg}{1}*\dfrac{2\ mL}{500\ mcg}*\dfrac{1000\ mcg}{1\ mg}[/tex]

Micrograms (mcg) will be cancelled out.

[tex]mL\ to\ administer=\dfrac{0.6\ mg}{1}*\dfrac{2\ mL}{500\ \not{mcg}}*\dfrac{1000\ \not{mcg}}{1\ mg}[/tex]

Milligrams (mg) will be cancelled out.

[tex]mL\ to\ administer=\dfrac{0.6\ \not{mg}}{1}*\dfrac{2\ mL}{500}*\dfrac{1000}{1\ \not{mg}}[/tex]

Only millilitres (mL) remains, which is the units our final answer needs to be in. Solve.

[tex]mL\ to\ administer=\dfrac{0.6}{1}*\dfrac{2\ mL}{500}*\dfrac{1000}{1}[/tex]

[tex]mL\ to\ administer=\dfrac{2.4\ mL}{1}[/tex]

Therefore, 2.4 millilitres of digoxin must be administered for the correct dose.

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