The Apprentice’s Guide to Physics: An Introductory Quest Through the Mechanics of the Universe

Unit prefixes are the verbal runes that shrink or stretch your units with a single syllable. They’re shortcuts to tame unwieldy measurements without changing their essence. Instead of writing out \(3000\) meters, you can invoke the prefix kilo- to conjure \(3\) kilometers. Instead of whispering \(0.000000001\) seconds, you can say \(1\) nanosecond and sound like a seasoned chronomancer.

Prefixes are always attached to units, not to the raw numbers themselves. You won’t hear "nano" on it’s own; it always comes with a unit like "meter" or "second." This is because prefixes are like magical modifiers that alter the scale of the unit, not the number itself.

If you want to use unit prefixes in your written spells, each prefix has its own symbol. For example, the prefix kilo- is represented by \(\text{k}\text{.}\) A distance of 3 km can be written more compactly as \(3\,\text{km}\text{.}\) Likewise, a time interval of 1 ns can be written as \(1\,\text{ns}\text{.}\)

Note that there are also two ways to verbalize unit prefixes: the prefix name and the decimal name. The prefix name is the official SI term used in scientific contexts, like mega- or nano-. The decimal name is the everyday term that describes the quantity in more familiar terms, like "million" or "billionth."

You might wonder: if we can say “megagrams” instead of “a million grams,” why do we need both? The key is that they serve different roles in communication. The prefix name (like mega-) is part of the official SI system. It’s used when naming and writing units in scientific work: megameters, milliamps, nanoseconds. These are concise, precise, and standardized.

The decimal name (like “million”) isn’t part of the unit itself, it’s just how we describe the value of a number in everyday terms. You’ll often hear it in speech, estimates, or media. Saying “a billion cells” or “a trillion dollars” is more natural for general audiences to understand compared to “gigacells” or “teradollars.”

So both ways are valid, but they’re used in different contexts. And when you’re fluent in both, you can navigate smoothly between scientific scrolls and everyday storytelling.

Bonus Trick: Poer of \(10\) notation. When converting prefixed units to base units, you can use powers of ten to simplify the process. Each prefix corresponds to a specific power of ten. For example, \(550\, \text{nm}\) turns into \(550 \times 10^{-9}\, \text{m}\text{.}\)

It’s customary to not stack unit prefixes. For example, if you have \(8\) million grams, you would not typically say \(8\) kilokilogram, instead you would say \(8\) megagrams or \(8 \times 10^{6}\) grams.

Be careful when communicating with synthetic beings, since unit prefixes used to represent different things in binary code. For example, \(1\) kilobyte once used to be defined as \(1024\) bytes. However, those ancient scrolls have been updated to match our standard unit prefix notation. Now \(1\) kilobyte is \(1000\) bytes, and \(1\) kibibyte is \(1024\) bytes. It’s best to extablish a common understanding before engaging in data transfer.

A Parting Word

One prefix to scale them all, one prefix to name them, one prefix to tame them all, and with the units frame them.