Study Guide

Types of Numbers Introduction

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Types of Numbers Introduction

You've been working with numbers ever since you learned your 1s, 2s, and 3s. (Hopefully you've got those down by now or the rest of this is going to be a blur.) For years, you've been seeing the same old numbers pop up again and again, and you might suspect that not much has changed in the world of mathematics since Euclid broke onto the scene.

But in reality, numbers as we know them today are the result of many centuries of problem-solving. As problems have gotten gnarlier and more complex, we've actually had to invent new kinds of numbers in order to solve the new kinds of problems. To keep written math short and sweet with all these new numbers, mathematicians have also devised a dizzying number of acronyms and abbreviations. We're pretty sure these guys would have been some pretty phenomenal texters: e > 32 – 4i(2x) + loljk(omg!).

There are different ways of writing numbers depending on the situation, such as fractions and decimals. It's okay to say you're going to down "half a gallon of milk" (although we don't recommend actually doing it), but to say you're going to drink "0.50 gallons of milk" will probably get you some strange looks. On the other hand, asking your mom for $0.50 (you find she's more generous when you keep it realistic) makes more sense than requesting half a dollar.

On the practical side of things, numbers and operations allow us to tip the waiter, bake cupcakes, calculate sales tax, and balance a checkbook. On the impractical side of things, they allow us to concoct a secret potion that's exactly the right parts eye of newt to toe of frog. You can't just wing those secret potions.

Types of Numbers Resources


Algebra: Real Numbers
Want to put in a little extra time identifying your different number types? Click here for some practice lessons, and if you have any questions, you can email a tutor. Your tutor, at least, is guaranteed to be rational.

Function Machine
This is great for honing your pattern-spotting skills. Input numbers in the function machine, see which numbers come out, and try to determine the pattern. If you get "paisley," you’re doing it wrong.


Types of Real Numbers
More of a visual learner? No problem. Here’s a video that uses Photoshop and a pretty green drawing tool to illustrate the different number types (will also be available in mauve and cyan in Spring 2016).  

Negative Exponents
Exponents got you down? Let this instructional guide help you lift them back up to where they’re supposed to be.


Crack Hacker’s Safe
This game is another good tool for helping you find patterns—not only in numbers, but in colors and shapes as well. (Okay, so that part is a little second grade, but at least it isn't drab and boring.)

Mystery Picture
Solve the problems correctly and uncover parts of a picture. When you're done, you can print it out, frame it, and hang it on your wall. Or not.

The Factor Game
This is a two-player game to help you practice factoring, so we hope you have a friend around who can play it with you. Or a mom. Or a pretty sharp Pomeranian.

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