Picture someone in a lab telling you a result is "25". Twenty-five what? Millilitres? Litres? Grams? Without the unit, the number means almost nothing. That sounds obvious, but a surprising number of lab mistakes come down to exactly this: a unit lost somewhere along the way.
The unit is half the answer
"25" is not a measurement. "25 mL" is. The unit tells you what kind of thing you measured and how big each step of it is. And units follow the same arithmetic as numbers: they multiply, divide and cancel. That turns out to be very useful.
Let the units check your work
Here is the trick chemists use, and it works for cooking, travel and money too. Every conversion can be written as a fraction that equals one. Since 1 litre is 1000 millilitres, "1 L over 1000 mL" equals one. Multiply by it and you change the unit without changing the amount.
Write every number with its unit, set up the fractions so the units you do not want cancel out, and look at what is left at the end. If you wanted grams and you are left with something strange, like grams squared per mole, you know the setup is wrong before you have even reached for the calculator.
Right by accident
A real question posted on a chromatography forum in December 2024 shows how this plays out. A technician needed to make up a standard solution and worked out the mass to weigh. That first step came out a thousand times too small: milligrams where it should have been grams. The next step, turning the mass into a volume, was off by a thousand the other way. The two mistakes cancelled, and the final number happened to be right.
Lucky? Yes. Safe? No. A calculation that is right by accident will not be right next time. Written with units at every step, both mistakes would have stood out immediately.
Watch out for "ppm"
Some units hide what they mean. "Parts per million" can mean milligrams per kilogram, milligrams per litre, or something else again, depending on who is writing. In plain water those are almost the same; in seawater, soil or a solvent they are not. The US National Institute of Standards and Technology does not accept "ppm" for stating values for exactly this reason. Whenever you see it, ask: parts of what, per what?
When units were not carried
In 1999 NASA lost a Mars probe because one piece of software produced numbers in imperial units while another expected metric ones. In 1983 a passenger jet in Canada ran out of fuel in flight because a fuel density in pounds per litre was used as if it were kilograms per litre; the crew glided it safely to a landing at an old airbase in Gimli, Manitoba. In both cases every number was copied correctly. Only the unit was lost.
Why this matters to you
Medicine doses, recipes, fuel, mortgage rates: all of them are a number and a unit. The habit is simple and almost free. Write the unit every time, let the units cancel, and if the one left at the end is not the one you expected, stop and look again.
Want the full lesson, with worked calculations, practice problems with the units shown, and the questions?
Read the full lesson → Free: sign in with your email, no password.
References
- A. Thompson, B. N. Taylor, Guide for the Use of the International System of Units (SI), NIST Special Publication 811 (2008).
- "Standard prep using liquids", Chromatography Forum, December 2024.
- Mars Climate Orbiter Mishap Investigation Board, Phase I Report (1999).
- Air Canada Flight 143 (the "Gimli Glider"), 23 July 1983.