A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which eighth graders have to determine how many millilters (mL) are in 4.6 liters (L). (If anyone from this particular state department is reading this, the sample form LM has “millimeters” in the question, not “milliliters,” a minor typo that will not bother us too much.)
This is a straightforward question, since both units use the metric system. All we really have to know is the meaning of the prefixes. In the metric system, a complete table of prefixes can be found at
http://www.simetric.co.uk/siprefix.htm
Such a comprehensive table is probably overkill, but there it is for your reference. A very common mistake with the metric prefixes is that students think the prefix “milli-” is related to the English word “million.” It really is related to “thousandths.” Oddly enough, that mistake, which is quite common in classrooms, is not presented as one of the answer choices.
The problem asks how many milliliters (mL) are in 4.6 liters (L). An abbreviated table of Le Système International d’Unités (SI) prefixes is shown below, along with their multipliers:
| Prefix | Multiplier | Abbreviation |
| mega- | 1,000,000 | M |
| kilo- | 1,000 | k |
| deci- | 0.1 | d |
| centi- | 0.01 | c |
| milli- | 0.001 | m |
| micro- | 0.000 001 | µ |
The way to read this table is like so: Suppose you have 20 kilometers (km). You look at the table and see that the multiplier for “kilo-” is 1,000. You say: “20 kilometers (your problem) is 20 × 1,000 (the multiplier in the table) = 20,000 meters (the base unit in your problem).
If we have 4.6 L and we need to know how many mL that is, we need to multiply by the inverse of 0.001, which would be 1,000. We do this because the prefix “milli-” means the number is already multiplied by 0.001, so to reverse that, we multiply by the inverse.
Thus, 4.6 L = 4.6 × 1,000 = 4,600 mL.
What we did, since we started with the base unit (L) and had to convert it to the unit with the prefix (mL), we needed to multiply by the inverse of the number in the table. Since the number in the table for our prefix (milli-) was 0.001, we needed to multiply by 1,000 (the inverse of the multiplier in the table).
Common sense takes over
Another way to look at the conversion is that 1 millimeter (mm) is much smaller than 1 meter (m). As a matter of fact, 1 mm is only 1/1000th the size of 1 m. So when converting L to mL above, you should get a much larger number, since liters are much bigger (a thousand times bigger) than milliliters.
If you would like more practice on unit conversion problems, visit our online library at VoxLearn.org and search for “unit conversion.”