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Take the PAIN out of math part 2.1 (field trip 1)

## What is “number base” and why does it matter?

Today, we are going on a field trip in time and space. The year is 2055, and scientists have figured out a way to create little delicious protein packages, resembling eggs. That’s right, chickens no longer do the job for us, they now live in wilderness preserves created just for creatures who previously lived on farms.

Why do we care? Well because we are visiting an egg factory, and if there were chickens there, my allergies would drive me craaaazy!

What do eggs have to do with math? Wait and see!

Well, the first building we go into is the decimal egg factory. Here, eggs are precisely 6 centimeters in size. They are also packaged in cartons having 10 eggs in them. Then 10 cartons are packaged into a box. 10 boxes are arranged on a flat. And 10 flats are stacked into a shipping crate. 10,000 eggs in all, whew that’s a lot of eggs! The tour guide explains, “some folks still like to count using the old decimal system”.

Now the next building is why we are here! This is the “dozenal” (or base twelve) egg factory. Here, eggs are 2.5 inches and packed into cartons of twelve, and twelve cartons to a box, twelve boxes to a flat, and twelve flats to a shipping crate. As you might imagine, if we tried to use the old decimal system to do math here, it might be hard to do in our head. I don’t know what 12×12×12×12 is right away. But not to worry. Here they use dozenal math!

So how does dozenal math work? It’s easy! But you first have to define your numbers. We have the usual 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. But we create a new symbol for ten and eleven. Let’s let “t” be ten and “e” be eleven. There’s other symbols we can use but this will keep it easy. So now we have 0, 1, 2, … , 8, 9, t, and e.

Here’s the tricky thing to get used to. When we look at a number like 13 in the decimal system, it means “one 10 and three 1’s”. But if we are in dozenal, 13 means “one **twelve** and three 1’s”.

Okay before you get too concerned, let me show you how this makes sense. Let’s go back to the decimal factory for a second and write down 13, and we’re gonna ask a worker there to demonstrate what 13 means in terms of eggs. They speak decimal in that factory, so she goes over to a pile and brings back her answer. One carton of ten eggs, and three individual eggs. Since there are ten eggs in their carton, we have…