数学英语 38 What Do Prefixes Mean in Math? - Part 1

by Jason Marshall

We use a lot of math words in our day-to-day lives without really understanding what they mean or where they come from. For example, prefixes 2 like “mega,” “giga,” and “tera” that we use to describe computer hard drive sizes (think “megabyte,” “gigabyte,” and “terabyte”) have specific meanings and uses that go far beyond the world of computers. So today we’re taking some time to explore the language of mathematical prefixes.

The Metric System of Units and Prefixes

To start things off, let’s take a minute to talk about the different systems of units commonly used around the world for making measurements. The first system is called the imperial system and uses units of miles, yards, feet, and inches for measuring distances. This system is quite familiar to you if you grew up in the US, but probably not so much if you grew up almost anywhere else. And that’s because the main system of units used around the world—including by nearly all scientists and mathematicians—is called the SI system (which stands for “International System”), or more commonly, the metric system. Why is the metric system so popular? Well, in many ways it’s because of its simplicity 3. So why is it so simple? One word: prefixes. Here’s what I mean.

According to an international agreement first made in 1795, the metric unit of distance is the meter, and that means that all other lengths measured in the metric system are based on the meter. You’re already quite familiar with this fact since you’ve seen meter sticks divided up into centimeters and millimeters, and you’ve measured longer distances in kilometers. What’s the common feature in all these words: centimeters, millimeters, kilometers? Of course it’s the “meter” part. So what’s going on here? Well, that international agreement that established the length of the meter in 1795 also established a group of six prefixes that could be tacked 4 onto the unit meter to modify its meaning.

Prefixes for Numbers Smaller Than One

Those original six prefixes were

milli,

centi,

deci,

deca,

hecto, and

kilo.

So, the idea was to divide a meter up into one thousand equally sized smaller pieces, and to call each of these one milli-meter. Sensibly, the prefix 1 “milli” comes from the Latin word “mille” meaning one thousand. A millimeter is therefore one-thousandth of a meter. If you were instead measuring something a little larger, then it would make sense to measure lengths in some unit sized between a millimeter and a meter, so the centi-meter is defined to be one-hundredth of a meter (and therefore also 10 millimeters). Again, the prefix “centi” is sensibly named since it comes from the Latin “centum” meaning one hundred (the same Latin root is in the word percent). A centimeter is therefore one-hundredth of a meter.

So the general idea of the metric system is to define a base unit (for example meters) and then create other units (like centimeters and millimeters) from this base unit that are multiples of 10 larger and smaller. That way, depending on the size of the thing you’re measuring, you can choose a conveniently sized unit so that you don’t have to write bunches of zeros everywhere. For example, if you are on a field expedition measuring the sizes of tiny bugs 6, when you find a 2 millimeter long tiny bug 5 you can simply write its length as “2 millimeters” instead of the rather cumbersome 7 “0.002 meters.” It’s simply a much more convenient system! And to top things off, unlike the imperial system, it’s all based on multiples of 10—making it really easy to do calculations too!

Prefixes for Even Smaller Numbers

A millimeter is pretty small, but how about even smaller lengths? Are there metric prefixes for those too? Absolutely, the metric system has you covered there as well. The prefix “micro,” which comes from the Greek word meaning “small,” is used to denote one-millionth. So a micrometer is one-millionth of a meter. And that’s pretty small—the width of a human hair can be anywhere between 20 and 80 micrometers! But how about even smaller lengths? Sure, we can go down another factor of one-thousand in size to the nanometer (“nano” is based on the Greek word for “dwarf”). So a nanometer is one-thousandth of a micrometer, or one-billionth of a meter! You’ve probably heard the word “nano” tossed around lately in the context of nanotechnology. And now you know exactly where this word comes from—it simply has to do with tiny technology built on size-scales of a billionth of a meter—which is about 50,000 times smaller than the width of a human hair!

Do the prefixes go even smaller? Yep, there’s “pico,” then “femto,” “atto,” “zepto,” and finally “yocto.” But it’s unlikely you’ll ever hear about anything that small. After all, the diameter of the nucleus 8 of a hydrogen atom is on the order of a femtometer, and an attometer, zeptometer, and yoctometer are each successively one-thousand times smaller than that!

Prefixes for Larger Numbers

But what about the prefix “kilo” and the rest of the original six 1795 prefixes? And what about “mega,” “giga,” and “tera” that we talked about in relation to hard drive sizes? Well, unfortunately we’re out of time for today. But don’t worry, we’ll talk about all the prefixes for numbers larger than one soon—including the story of an interesting newcomer that’s been getting a lot of press lately. Oh, one more thing: I should mention that while we’ve been talking about prefixes in the context of length (in particular how they can be used to modify a meter), they can be used with other units too. For example, we can measure things that happen very quickly in milliseconds, microseconds, or even nanoseconds. The prefixes work the same way.

Wrap Up

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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!