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Using dimensional analysis, perform the following dosage calculation, expressing your answer in mL, rounded to the nearest tenth.

An IV additive has a dosage strength of 20 mEq per 20 mL. A dosage of 19 mEq has been ordered. How many mL will be needed?

(Simplify your answer completely.)

Answer :

We begin by writing the conversion factor using the dosage strength:

[tex]$$
\frac{20 \text{ mL}}{20 \text{ mEq}}
$$[/tex]

Since we want to convert from milliequivalents (mEq) to milliliters (mL), we multiply the ordered dosage by the conversion factor. The ordered dosage is 19 mEq. Thus, the calculation is:

[tex]$$
19 \text{ mEq} \times \frac{20 \text{ mL}}{20 \text{ mEq}}.
$$[/tex]

Notice that the unit mEq cancels:

[tex]$$
19 \times \frac{20}{20} \text{ mL}.
$$[/tex]

Since [tex]$\frac{20}{20} = 1$[/tex], the result simplifies to:

[tex]$$
19 \text{ mL}.
$$[/tex]

Rounded to the nearest tenth, the final answer is:

[tex]$$
19.0 \text{ mL}.
$$[/tex]

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