Metric Prefix
A metric prefix is a word part such as kilo-, centi-, or milli- that scales a base unit by a power of ten.
Definition
A metric prefix is a short word part added to the front of a unit to make it bigger or smaller: kilo- means $1000$ of something, centi- means one hundredth, and milli- means one thousandth. Each prefix multiplies a base unit by a fixed power of ten, from kilo- ($10^3$), hecto- ($10^2$), and deka- ($10^1$) down through deci- ($10^{-1}$), centi- ($10^{-2}$), and milli- ($10^{-3}$), with mega-, giga-, micro-, and nano- for larger and smaller scales, and converting between prefixed units means moving the decimal point by the difference in exponents. A prefixed unit is treated as a single symbol, so $\text{cm}^3$ means $(\text{cm})^3 = 10^{-6}\ \text{m}^3$. Prefixes are chosen so the numerical value falls in a readable range and are interchangeable with scientific notation, which is preferred in calculations because exponents combine cleanly.
Example
A kilogram is $1000$ grams, a centimeter is one hundredth of a meter, and a milliliter is one thousandth of a liter. A cart traveling $1.5\ \text{m}$ down a ramp has gone $150\ \text{cm}$, $1500\ \text{mm}$, or $0.0015\ \text{km}$, the same length with a different label. A cell $12\ \mu\text{m}$ across is $1.2 \times 10^{-5}\ \text{m}$, and a volume of $1\ \text{cm}^3$ converts to $(10^{-2}\ \text{m})^3 = 10^{-6}\ \text{m}^3$, so $1000\ \text{cm}^3 = 10^{-3}\ \text{m}^3 = 1\ \text{L}$; forgetting to cube the prefix is a factor-of-$10^4$ error.
Key Insight
Three prefixes cover almost everything in a middle-school lab: kilo- ($1000$), centi- ($1/100$), and milli- ($1/1000$). The prefix ladder (kilo, hecto, deka, base, deci, centi, milli) is one decimal place per step, moving the decimal right going down and left going up. Prefixes on squared and cubed units are the single most common conversion trap, because the prefix sits inside the power and gets squared or cubed too.