Module 2 of 14 · 12 min
Percentage, ratio strength & ppm
Labels state strength as %, as 1:x, as mg/mL or as ppm — and you must move between them instantly: epinephrine 1:1000, lidocaine 2%, fluoride 0.7 ppm, a 37% w/w acid. Exams love questions where the trick is just converting the expression.
🧠 Percent to mg/mL: times ten (2% → 20 mg/mL). Ratio 1:x to percent: 100 over x.
📌 Memorize these
- $1\%\ \text{w/v}$
- $1\,\text{g}/100\,\text{mL} = 10\,\text{mg/mL}$
- $1{:}1000$
- $0.1\% = 1\,\text{mg/mL}$
- $1{:}x$
- $\tfrac{100}{x}\,\%$
- $1\,\text{ppm}$
- $1\,\text{mg/L} = 0.0001\%$
- $1\,\text{ppb}$
- $1\,\text{mcg/L}$
- grams
- $\text{mL}\times\text{SG}$
- $\%\ \text{w/v}$
- $\%\ \text{w/w}\times\text{SG}$
Percent always means 'per 100', and the w/v, w/w or v/v label tells you the units: w/v = g per 100 mL (solids in liquids — assumed if nothing is said), w/w = g per 100 g (creams, ointments, powders), v/v = mL per 100 mL (liquids in liquids, e.g. alcohol).
Ratio strength $1{:}x$ is just a very dilute percentage written the other way up: 1 g in $x$ mL (or 1 g in $x$ g for solids). So $1{:}1000 = \frac{1\,\text{g}}{1000\,\text{mL}} = 1\,\text{mg/mL} = 0.1\%$. To convert, use $\% = \frac{100}{x}$ and $x = \frac{100}{\%}$.
Parts per million: $1\,\text{ppm} = 1\,\text{g}$ in $10^6\,\text{mL}$ $= 1\,\text{mg/L} = 0.0001\%$. Parts per billion (ppb) is a thousand times smaller: $1\,\text{ppb} = 1\,\text{mcg/L}$.
Specific gravity (SG) is density relative to water, so numerically $\text{SG} = $ density in g/mL. Use it to switch between weight and volume ($\text{g} = \text{mL}\times\text{SG}$) and so between w/w and w/v: $\%\,\text{w/v} = \%\,\text{w/w}\times\text{SG}$.
🧭 The method
- 1Identify the type: w/v, w/w, v/v, ratio strength or ppm.
- 2Rewrite the strength as a fraction with units (e.g. 2% w/v → 2 g/100 mL; 1:5000 → 1 g/5000 mL).
- 3If weight and volume are mixed (w/w data, volume asked, or vice-versa), use SG: g = mL × SG.
- 4Multiply by the quantity asked about so units cancel; convert g ↔ mg at the end.
Before each reveal, predict the next step — then check.
Epinephrine injection is labelled 1:1000. (a) What is its concentration in mg/mL and in %? (b) What volume delivers a 0.3 mg dose?
- 1
Ratio strength 1:1000 for a solution means 1 g in 1000 mL.
$$1{:}1000 = \frac{1\,\text{g}}{1000\,\text{mL}}$$ Convert g to mg so the concentration is in useful units.
$$\frac{1\,\cancel{\text{g}}}{1000\,\text{mL}}\times\frac{1000\,\text{mg}}{1\,\cancel{\text{g}}} = 1\,\text{mg/mL}$$As a percentage: % = 100 / x.
$$\frac{100}{1000} = 0.1\%\ \text{w/v}$$Volume for the dose, with mg cancelling.
$$0.3\,\cancel{\text{mg}}\times\frac{1\,\text{mL}}{1\,\cancel{\text{mg}}} = 0.3\,\text{mL}$$
Same method — the last steps are yours. Work on paper, then reveal.
How many mg of lidocaine are in 7.5 mL of a 2% w/v solution?
- 1
Write 2% w/v as a fraction.
$$2\% = \frac{2\,\text{g}}{100\,\text{mL}}$$ - 2
Your turn
Now you: convert to mg/mL (shortcut: % × 10).
Work it out on paper, then reveal.
$$\frac{2000\,\text{mg}}{100\,\text{mL}} = 20\,\text{mg/mL}$$ - 3
Your turn
Now you: multiply by the volume.
Work it out on paper, then reveal.
$$7.5\,\cancel{\text{mL}}\times 20\,\frac{\text{mg}}{\cancel{\text{mL}}} = 150\,\text{mg}$$
Type your number. Your first try decides when this module comes back for review.
How many grams of dextrose are in 500 mL of D10W (dextrose 10% w/v)?
10% w/v = 10 g in every 100 mL.
= 50 g
Fluoridated drinking water contains 0.7 ppm fluoride. How many mg of fluoride are in 2 L?
1 ppm = 1 mg per litre of water.
= 1.4 mg
Express a 0.02% w/v solution as a ratio strength 1:x. Enter x.
x = 100 / %. Watch the decimal: 0.02, not 0.2.
= 5000
How many mg of potassium permanganate are needed to make 250 mL of a 1:5000 solution?
1:5000 = 1 g per 5000 mL. Find the grams for 250 mL, then convert to mg.
= 50 mg
Glycerin has a specific gravity of 1.25. What volume of glycerin weighs 50 g?
g = mL × SG, so mL = g ÷ SG. A heavier-than-water liquid takes up LESS volume than its weight in grams.
= 40 mL
Concentrated hydrochloric acid is 37% w/w with a specific gravity of 1.18. How many grams of HCl are in 100 mL?
w/w is per 100 g of SOLUTION, not per 100 mL. Weigh the 100 mL first.
= 43.66 g
⚠️ Tricky
Epinephrine is supplied as a 1:1000 solution. How many mL contain a 250 mcg dose?
1:1000 = 1 g in 1000 mL. What is that in mg/mL? And what is 250 mcg in mg?
= 0.25 mL
⚠️ The trap: Dividing 250 (mcg) by 1 (mg/mL) without converting gives 250 mL.
⚠️ Tricky
Sorbitol solution is 70% w/w with a specific gravity of 1.29. How many grams of sorbitol are in a 473 mL bottle?
w/w means grams per 100 g of SOLUTION. Turn the volume into a weight first.
= 427.12 g
⚠️ The trap: Treating 70% w/w as 70% w/v (70 g per 100 mL) gives 331.1 g.
⚠️ Tricky
A water sample contains 2.5 ppm of lead. How many micrograms of lead are in 200 mL of the sample?
1 ppm = 1 mg per litre. Then convert both the volume and the answer unit.
= 500 mcg
⚠️ The trap: Reading ppm as mcg per litre (that is ppb) gives 0.5 mcg — a thousand-fold underestimate.
⚠️ Tricky
Lidocaine 2% with epinephrine 1:200,000 is used for a nerve block in a 60 kg adult. The maximum lidocaine dose with epinephrine is 7 mg/kg. What is the maximum volume that may be injected?
The epinephrine ratio is not needed. 2% w/v = how many mg/mL?
= 21 mL
⚠️ The trap: Reading 2% as 2 mg/mL gives 210 mL — ten times the safe maximum.
⚠️ Tricky
5 g of a drug is dissolved in 95 mL of purified water; the finished solution measures 98 mL. What is its strength in % w/v?
% w/v is grams per 100 mL of the FINAL solution — not of the solvent, and not 5 + 95.
= 5.1 % w/v
⚠️ The trap: Dividing by the 95 mL of water used gives 5.26%.
🕵️ Spot the mistake
How many mg of drug are in 4 mL of a 0.5% w/v eye drop?
A student wrote
⚠️ Traps examiners set
- Treating % as mg/mL — 1% is 10 mg/mL.
- Assuming w/w equals w/v: they are only equal when SG = 1.
- Multiplying by SG when you should divide (mL = g ÷ SG).
- Inverting a ratio strength: 1:5000 is weaker than 1:500, not stronger.
- Reading ppm as mg/mL instead of mg/L.
💬 Explain it in your own words
Explain in your own words why 1:1000 and 0.1% are the same strength, and why a bigger x in 1:x means a weaker solution.