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Med math · 5 free problems

Oral liquid dosage practice: mg per mL labels

A liquid label gives an amount in a volume. Multiply the ordered amount by the labeled volume over the labeled amount, then apply the rounding rule the exercise states.

Fictional labels. Round as each question says. How to round

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Oral liquids: work through the set

Question 1 of 5

Liquid labeled per 5 mL

A fictional oral-liquid exercise requests 210 mg for one dose. The practice label states 140 mg in 5 mL. What volume contains 210 mg? Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 7.5 mL.

210 mg × (5 mL / 140 mg) = 7.5 mL. The label gives 140 mg per 5 mL, so keep those two numbers together.

Check: 140 mg ÷ 5 mL = 28 mg/mL; 7.5 mL × 28 mg/mL = 210 mg.

If you got 1.5 mL: 210 ÷ 140 = 1.5 counts portions of the labeled 5 mL volume. Multiply by 5 mL to find the volume.

Question 2 of 5

Round the final liquid volume

A fictional oral-liquid exercise requests 285 mg for one dose. The practice label states 175 mg in 5 mL. Calculate the volume in mL. For this exercise, round the final answer to the nearest tenth of a mL. Do not round intermediate calculations.

Worked solution and answer

Answer: 8.1 mL.

285 mg × (5 mL / 175 mg) = 57/7 mL = 8.142857… mL. Round the final result to 8.1 mL.

Check: The concentration is 35 mg/mL. Before rounding, (57/7 mL) × 35 mg/mL = 285 mg. The rounded result represents 283.5 mg; the small difference comes from the requested rounding. This is an arithmetic exercise, not an assessment of whether that difference is clinically acceptable.

If you got 8 mL: Rounding 285 ÷ 175 to 1.6 before multiplying by 5 changes the final result. Keep full precision until the last step.

Question 3 of 5

A volume below 1 mL

A fictional oral-liquid exercise requests 3.7 mg for one dose. Its practice label states 25 mg in 1 mL. Calculate the volume in mL. For this exercise, round the final answer to the nearest hundredth of a mL. Do not round intermediate calculations.

Worked solution and answer

Answer: 0.15 mL.

3.7 mg × (1 mL / 25 mg) = 0.148 mL. The thousandths digit is 8, so the final answer rounds to 0.15 mL.

Check: 0.148 mL × 25 mg/mL = 3.7 mg before rounding. The requested amount is less than the amount in 1 mL, so the calculated volume should be below 1 mL.

If you got 0.1 mL: That is rounding to tenths. This question asks for hundredths. Write the leading zero in 0.15 mL.

Question 4 of 5

Liquid labeled 250 mg per 5 mL

A fictional oral-liquid exercise requests 400 mg for one dose. The practice label states 250 mg in 5 mL. What volume contains 400 mg? Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 8 mL.

400 mg × (5 mL / 250 mg) = 8 mL. The mg units cancel.

Check: 8 mL × (250 mg / 5 mL) = 400 mg.

If you got 1.6: That is 400 ÷ 250 without the 5 mL. Multiply by the volume that holds the labeled amount.

Question 5 of 5

Convert grams, then use the label

A fictional oral-liquid exercise requests 0.2 g for one dose. The practice label states 125 mg in 5 mL. What volume contains 0.2 g? Use 1 g = 1,000 mg. Give the exact answer in mL; no rounding is needed.

Worked solution and answer

Answer: 8 mL.

First 0.2 g × (1,000 mg / 1 g) = 200 mg. Then 200 mg × (5 mL / 125 mg) = 8 mL.

Check: 8 mL × (125 mg / 5 mL) = 200 mg = 0.2 g.

If you got 0.008: You used 0.2 as if it were milligrams. Convert grams to milligrams before matching the label.

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