数学英语 39 What Do Prefixes Mean in Math? - Part 2

by Jason Marshall

A few weeks ago, we began talking about the meaning of prefixes 2 in math. In particular, we talked about the prefixes used in the metric system to represent lengths smaller than one meter. Today, we’re going to continue this topic by talking about the metric prefixes used to describe lengths much longer than one meter. And, since we’re chatting about big numbers, we’ll also talk a bit about the future of a recently proposed prefix 1 for describing really big numbers.

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Review of Metric Prefixes

In the first part of this series, we introduced some of the logic 3 behind the metric system of units—that is, the system of units established in 1795 and now used by the majority of the world to measure lengths in meters, centimeters, millimeters, and a bunch of other units based upon the meter. We also talked about the fact that this whole system of units has been extended by using a set of internationally agreed upon prefixes. In particular, we talked about the various prefixes used to break the meter up into smaller pieces. For example, a centimeter is one-hundredth of a meter, a millimeter is one-thousandth of a meter, the micrometer and nanometer are one-millionth and one-billionth of a meter, and there are more almost unfathomably tiny lengths continuing on from there.

But why do we need these other units? Why aren’t all lengths just measured in meters? Well, it’s simply because they make it a lot easier to write and talk about really small lengths. For example, it’s a lot easier to say that a typical human hair is between 20 and 80 micrometers long, rather than to say that it’s between 0.00002 and 0.00008 meters long—wouldn’t you agree?

The Original Six Metric Prefixes

We’ve also talked about the fact that the original six prefixes defined for use in 1795 were:

“milli,”

“centi,”

“deci,”

“deca,”

“hecto,” and

“kilo.”

We’re familiar with three of these (“milli,” “centi,” and “kilo”), but I bet most of you have never even heard of “deci,” “deca,” and “hecto”—until recently, I hadn’t either! And that’s simply because they’ve long fallen out of favor. But what were they originally intended for? Well, the decimeter represents a length of one-tenth of a meter (that is, 10 centimeters), the decameter represents a length of 10 meters, and the hectometer represents a length of 100 meters. My guess is that people found it plenty convenient to say that something is 30 centimeters, and didn’t really need the option of calling it 3 decimeters too.

Prefixes for Numbers Larger Than One

But the one thing we haven’t talked about yet are the prefixes used to describe numbers larger than one. Actually, you’re probably very familiar with the first one of these, “kilo,” which is derived 4 from the Greek word “chilioi” meaning “thousand.” Given this, it should come as no surprise that one kilometer is 1000 meters, a kilogram is 1000 grams, and so on. So, what’s next? Well, “mega” comes from the Greek word meaning “great” and is used to represent numbers that are yet another 1000 times larger. In other words, a megameter is 1000 kilometers, or one million meters! So, how big is that? Well, it’s pretty big—the average distance from the Earth to the Moon is about 385 megameters.

In truth, we don’t often use “mega” to talk about distances, but it is used a lot in the computer world. Back in the day, the hard drive on my first computer was a “whopping” 850 megabytes. I really thought that was awesome 5 at the time, but it’s almost laughable now. But what exactly does it mean? It means that my hard drive was able to store 850 million bytes worth of information. It sounds like a lot, but these days hard drive sizes are measured in gigabytes or even terabytes. What’s that? Well, “giga” comes form the Greek word meaning “giant” and “tera” comes from the Greek word meaning “monster”—so they must represent some really big numbers! And they do: “giga” means 1 billion, and “tera” represents one trillion! So a one terabyte hard drive can store one trillion bytes of information. Just to give a bit more perspective on how big these numbers are, the 93-million mile distance from the Earth to the Sun is equivalent to about 150 gigameters or 0.15 terameters!

Prefixes for Incredibly Large Numbers

So what’s even bigger? Well, next comes the prefix “peta” meaning one quadrillion (which is a thousand trillion), then “exa” meaning one quintillion (which is a thousand quadrillion), and finally “zetta” and “yotta”—which are each successively one thousand times bigger! For comparison, the distance to the next big galaxy 6, Andromeda, is about 2.5 million light-years (meaning it’d take light 2.5 million years to travel there)—which is equivalent to about 24 zettameters. And the entire observable universe is on the order of a few hundred yottameters across.

Will More Metric Prefixes Be Added?

Interestingly, the “zetta” and “yotta” prefixes were only added to the metric mix in 1991, so development is still happening. In fact, there’s been an Internet-driven campaign to get the prefix “hella” officially recognized as meaning a number that’s 1000 times bigger than the prefix “yotta.” If that ever happens, the size of the observable universe would be a bit less than one hellameter. The “hella” movement began in Northern California where the word has long been used in phrases like: “That’s hella cool.” And lately, the movement has picked up some steam by getting a fair bit of national press coverage 7. The fine folks at Google have even incorporated the prefix “hella” into their online calculator! (Just go to Google and type in “1 hellameter in meters”.) So, will “hella” stick? I don’t know, but I for one hope that it does.

Wrap Up

Alright, that’s all the math we have time for today. Please email your math questions and comments to..................You can get updates about the Math Dude podcast, the “Video Extra!” episodes on YouTube, and all my other musings about math, science, and life in general by following me on Twitter. And don’t forget to join our great community of social networking math fans by becoming a fan of the Math Dude on Facebook.

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!