Why must measurements always be expressed with units?

Answer 1

If units are not specified in a stated measurement then the answer is ambiguous. This is because languages have more than one standard-size unit for every kind of measurement. For example, distance can be measured in inches, feet yards, and miles, or in centimeters, meters, and kilometers.

If only a number is given, without a unit, the reader or listener will likely not understand what you are trying to communicate. Although, that said, the context often lets you know, by convention, which units are meant. But where certainty is important, as in mathematics or science or engineering, the units must be stated.

Some examples:

Unclear:
- In a list of recipe ingredients: Sugar: 3. (3 cups, 3 tablespoons, or?)
- It will be at least 20 more before I finish. (20 minutes, hours, days, or?)
- How far away does your mother live? Just 2! (2 miles, 2 days' travel?)
- My sister is only 9.
- Start the retro-rocket burn exactly 200 above surface.

Clear by context:
- The speed limit in U.S. residential neighborhoods is 25. (You know it's 25 miles per hour.)
- I want 4 x 6 prints. (4 inches x 6 inches is a standard size of photographic prints; it's not likely the customer would mean prints 4 feet x 6 feet!)

Clear with units:
- Add 1/4 pound of butter. (Otherwise could be 1/4 cup or 1/4 stick.)
- My mother lives just 2 blocks away.
- My sister is only 9 weeks old!
- Fire the retro-rockets at 200 meters above the surface.

(The retro-rocket example is related to the finding of how a recent Mars probe was crashed into the surface of the planet. Engineers and programmers used different units for distance and failed to communicate that. The probe could not stop in time; an extraordinarily expensive spacecraft was lost.) because there are two units to measure density in to work out one in solids and the other in liquid.