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Percentage & Ratio Strength Practice Problems

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Percentage strength and ratio strength are two ways of saying how much drug is in a preparation. Percent weight-in-volume (% w/v), the more common of the two, is grams of drug per 100 mL. Ratio strength (1:X) conventionally means 1 gram of drug in X mL of preparation. Most other calculations on this site assume you can move between percent, ratio strength and mg/mL without stopping to think about it.

Formula% w/v = grams of drug per 100 mL  •  1:X ratio = 1 g in X mL  •  mg/mL ÷ 10 = % w/v
Worked example

Express 1:2,500 as a percentage. 1:2,500 means 1 g in 2,500 mL, so (1 ÷ 2,500) × 100 = 0.04% w/v.

Anchors to memorize: 1:1,000 = 0.1% (epinephrine), 1:10,000 = 0.01%.

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Correct 0/0
Percentage Strength
How many grams of active drug are in 50 mL of a 5% w/v solution? Round your answer to one decimal place.
g

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10 Percentage & Ratio Strength practice problems with worked solutions

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Problem 1: Percentage Strength

A solution contains 5 mg/mL of drug. What is its percentage strength (w/v)? Round your answer to two decimal places.

Answer 0.50 %

Solution
  1. 5 mg/mL = 500 mg per 100 mL = 0.5 g per 100 mL.
  2. Percent w/v = 0.5%.
  3. Rounded as the question asks: 0.50 %.

Fast rule: mg/mL ÷ 10 = % w/v (and % × 10 = mg/mL).

Problem 2: Ratio Strength

Express a 1:4,000 ratio strength as a percentage (w/v). Round your answer to three decimal places.

Answer 0.025 %

Solution
  1. 1:4,000 means 1 g of drug in 4,000 mL.
  2. Percent w/v = grams per 100 mL: (1 g ÷ 4,000 mL) × 100 mL = 0.025%.
  3. Rounded as the question asks: 0.025 %.

Anchors worth memorizing: 1:1,000 = 0.1% (epinephrine), 1:10,000 = 0.01%, 1:100,000 = 0.001%.

Problem 3: Percentage Strength

A solution contains 1 mg/mL of drug. What is its percentage strength (w/v)? Round your answer to two decimal places.

Answer 0.10 %

Solution
  1. 1 mg/mL = 100 mg per 100 mL = 0.1 g per 100 mL.
  2. Percent w/v = 0.1%.
  3. Rounded as the question asks: 0.10 %.

Fast rule: mg/mL ÷ 10 = % w/v (and % × 10 = mg/mL).

Problem 4: Ratio Strength

Express a 1:3,000 ratio strength as a percentage (w/v). Round your answer to three decimal places.

Answer 0.033 %

Solution
  1. 1:3,000 means 1 g of drug in 3,000 mL.
  2. Percent w/v = grams per 100 mL: (1 g ÷ 3,000 mL) × 100 mL ≈ 0.033%.
  3. Rounded as the question asks: 0.033 %.

Anchors worth memorizing: 1:1,000 = 0.1% (epinephrine), 1:10,000 = 0.01%, 1:100,000 = 0.001%.

Problem 5: Percentage Strength

How many grams of active drug are in 910 mL of a 2.5% w/v solution? Round your answer to one decimal place.

Answer 22.8 g

Solution
  1. 2.5% w/v = 2.5 g per 100 mL.
  2. Grams = 2.5 g/100 mL × 910 mL = 22.75 g.
  3. Rounded as the question asks: 22.8 g.

Problem 6: Ratio Strength

Express a 1:150 ratio strength as a percentage (w/v). Round your answer to three decimal places.

Answer 0.667 %

Solution
  1. 1:150 means 1 g of drug in 150 mL.
  2. Percent w/v = grams per 100 mL: (1 g ÷ 150 mL) × 100 mL ≈ 0.667%.
  3. Rounded as the question asks: 0.667 %.

Anchors worth memorizing: 1:1,000 = 0.1% (epinephrine), 1:10,000 = 0.01%, 1:100,000 = 0.001%.

Problem 7: Percentage Strength

A solution contains 150 mg/mL of drug. What is its percentage strength (w/v)? Round your answer to two decimal places.

Answer 15.00 %

Solution
  1. 150 mg/mL = 15000 mg per 100 mL = 15 g per 100 mL.
  2. Percent w/v = 15%.
  3. Rounded as the question asks: 15.00 %.

Fast rule: mg/mL ÷ 10 = % w/v (and % × 10 = mg/mL).

Problem 8: Ratio Strength

Express a 1:7,500 ratio strength as a percentage (w/v). Round your answer to three decimal places.

Answer 0.013 %

Solution
  1. 1:7,500 means 1 g of drug in 7,500 mL.
  2. Percent w/v = grams per 100 mL: (1 g ÷ 7,500 mL) × 100 mL ≈ 0.013%.
  3. Rounded as the question asks: 0.013 %.

Anchors worth memorizing: 1:1,000 = 0.1% (epinephrine), 1:10,000 = 0.01%, 1:100,000 = 0.001%.

Problem 9: Percentage Strength

A solution contains 10 mg/mL of drug. What is its percentage strength (w/v)? Round your answer to two decimal places.

Answer 1.00 %

Solution
  1. 10 mg/mL = 1000 mg per 100 mL = 1 g per 100 mL.
  2. Percent w/v = 1%.
  3. Rounded as the question asks: 1.00 %.

Fast rule: mg/mL ÷ 10 = % w/v (and % × 10 = mg/mL).

Problem 10: Ratio Strength

Express a 1:100,000 ratio strength as a percentage (w/v). Round your answer to three decimal places.

Answer 0.001 %

Solution
  1. 1:100,000 means 1 g of drug in 100,000 mL.
  2. Percent w/v = grams per 100 mL: (1 g ÷ 100,000 mL) × 100 mL = 0.001%.
  3. Rounded as the question asks: 0.001 %.

Anchors worth memorizing: 1:1,000 = 0.1% (epinephrine), 1:10,000 = 0.01%, 1:100,000 = 0.001%.

Sources and how far they go

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