Multiples and Submultiples of Standard Units
We use standard prefixes (like centi, deci, milli, etc.) to indicate multiples and submultiples of measurement units.
Instead of writing out a long string of zeros, which would only make things more complicated, you can simply use a prefix to show how large or small the number is that you're dealing with.
For example, writing 7 billion of any unit would require you to write the number seven followed by nine zeros. $$ 7,000,000,000 $$ It’s much simpler to write 7 Giga (G), or 7 x 109. $$ 7 \ G = 10^9 $$
Each of these prefixes represents a power of 10, meaning you multiply the base unit by that specific number.
To help you make sense of all these numbers and letters, here’s a table with the most common prefixes.
| Multiples | Submultiples | ||||
|---|---|---|---|---|---|
| deca / deka | da | 101 | deci | d | 10-1 |
| hecto | h | 102 | centi | c | 10-2 |
| kilo | k | 103 | milli | m | 10-3 |
| mega | M | 106 | micro | μ | 10-6 |
| giga | G | 109 | nano | n | 10-9 |
| tera | T | 1012 | pico | p | 10-12 |
| peta | P | 1015 | femto | f | 10-15 |
| exa | E | 1018 | atto | a | 10-18 |
| zetta | Z | 1021 | zepto | z | 10-21 |
| yotta | Y | 1024 | yocto | y | 10-24 |
Don’t get confused between $m$ for milli and $M$ for mega. One is a thousand times smaller, the other is a million times bigger. So yes, the difference is huge, even though it might seem trivial.
I know, you're probably wondering where you’d actually use these prefixes. Well, think about it next time you see that your USB drive holds 32 gigabytes of storage. That means it can store 32 billion bytes (characters), because one gigabyte (G) equals one billion bytes.
Let me make this clearer with an example. Suppose we’re talking about a data cable with a transfer speed of 500 megabits per second. What does that mean? Well, take the prefix mega (M) from the table I provided, which corresponds to 106, or one million. So, 500 megabits is simply 500 x 106 bits, or 500 x 1,000,000 bits, giving you a total of 500,000,000 bits per second.
$$ 500Mb/s = 500 \times 10^{6} \ b/s = 500 \times 1,000,000 \ b/s = 500,000,000 \ b/s $$
Now, imagine you have a powerful microscope and want to measure something tiny, like the length of a bacterium, which is about 2 micrometers (μm). The prefix micro (μ) represents 10-6, or one millionth. So, 2 micrometers is just 2 x 10-6, or 2 x 0.000001 meters, which equals 0.000002 meters.
$$ 2μm = 2 \times 10^{-6} \ m = 2 \times \frac{1}{10^6} \ m = 2 \times \frac{1}{1,000,000} \ m = 0.000002 \ m $$
See? With just a bit of multiplication or division, you can easily figure out the size of the object you’re working with.
All these units, prefixes, and powers of 10 might seem like a lot of numbers and symbols designed to complicate things, but in reality, they reflect something essential: our ability to make sense of complexity. Think about it: we live in a world where we can measure everything, from galactic distances in petameters (1015 meters) to the length of a virus in nanometers (10-9 meters).
Yet, even with all this ability to quantify, divide, and organize, we often remain confused. We’ve developed sophisticated tools to understand the world, but when it comes to sorting out our inner chaos, well, prefixes and powers of 10 just don’t quite cut it.
How to Convert Between Units Using Prefixes
So you want to convert from one unit to another? Great, let’s see if I can simplify the process for you and prevent any confusion.
Converting between units with standard prefixes is really just a matter of moving the decimal point. Basically, it’s about figuring out how much you need to multiply or divide when moving from one prefix to another.
To convert between units with prefixes:
- Identify the starting and target prefixes (e.g., kilo, mega, milli).
- Calculate the difference between the powers of 10 for the two prefixes. Between the larger power $ 10^a $ and the smaller one $ 10^b $. $$ \frac{10^a}{10^b} = 10^{a-b} $$
- Multiply or divide by that power of 10:
- If you're moving to a smaller prefix (e.g., from km to m), multiply.
- If you're moving to a larger prefix (e.g., from m to km), divide.
Here’s a tip: when converting, remember this rule of thumb: if you’re moving to a smaller prefix , multiply; if you’re moving to a larger one, divide.
Example 1
Convert 5.2 kilometers to meters.
Since kilo = 103, $ 5.2 \ km = 5.2 \times 10^3 = 5,200 \ meters $.
Easy, right? You just moved the decimal point three places to the right. It’s as simple as that… kind of like tuning out when Turk talks about basketball.
Example 2
Convert 350 milligrams to grams.
The milli prefix is 10-3, so a milligram is one thousandth of a gram.
Now, here’s the conversion:
$$ 350 \ mg = 350 \times 10^{-3}\ g = 0.350 \ g $$
All you did was move the decimal point three places to the left. Not too bad, right?
Example 3
Convert 0.025 gigabytes to megabytes.
Since a giga is 109 and a mega is 106, the difference is 103.
$$ \frac{10^9}{10^6} = 10^{9-6} = 10^3 $$
You’re converting to a smaller unit, so you need to multiply by 103:
$$ 0.025 \ GB = 0.025 \times 10^3 \ MB = 25 \ MB $$
If that’s still not clear or you feel overwhelmed, take a break, grab a coffee, and give it another go when you’re ready.
More exercises
