Ratio strength: one gram in so many millilitres

A ratio strength like 1:1000 means 1 gram in 1,000 mL, so the milligrams per millilitre are 1,000 divided by the number after the colon.

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What it is for

Ratio strengths turn up on the most concentrated products in the building, and the two labels that matter most look almost identical: 1:1000 and 1:10,000 differ by a factor of ten and by one character.

How to think about it

Write the ratio out as 1 gram in that many millilitres. Turn the gram into 1,000 mg. Divide by the millilitres. The whole thing collapses to one line: mg/mL is 1,000 over the number after the colon.

Worked example

1:1000 = 1 g in 1,000 mL = 1 mg/mL

One gram is 1,000 mg, spread through 1,000 mL.

1:10,000 = 1 g in 10,000 mL = 0.1 mg/mL

Ten times more dilute, one character apart on the label.

1:250 = 1 g in 250 mL = 1,000 mg / 250 mL = 4 mg/mL

The same arithmetic with any denominator.

mg/mL = 1,000 / the number after the colon

1,000 / 250 = 4. The rule behind all three lines above.

Your turn

Write 1:500 as a strength in milligrams per millilitre.

1,000 / 500 =  mg/mL

The trap

Reading 1:1000 as 1 mg in 1,000 mL. The 1 is a gram, so it is 1,000 mg in 1,000 mL, and a reading that makes it a milligram is a thousandfold error on the most concentrated shelf in the pharmacy.

Practise ratio strength on HoneA question on it now, a coding challenge where there is one, and it is remembered for review. Free, no email needed.