Beginning with the Basics: Numerical Bases:

If you want to review Maya numbers and arithmetic first, go here or here.

Number bases have been invented by cultures throughout the world to meet their day-to-day needs. As you probably know, we count in base ten. Why do you think base ten is convenient?

 

The answer is simple: All humans—at some stage—count on their fingers. However, even though most people have the same number of fingers, not everyone counts in base ten. Every culture decides how to group things in order to count them. Some cultures count using only one hand, so their base is five. (In several African languages, the word for five means “hand full.”) Other people count on both their hands and their feet, and use twenty as their base. Some Native Americans use base eight. Why eight? Count the number of spaces between your ten fingers.

 

Now imagine that you are visiting another planet where the intelligent beings are three-toed sloths. What bases do you think these beings would use for their sorting and counting?

 

The most likely bases for the sloths would be three (one foot), six (two feet), or twelve (all four feet).

 

If you understand the concept of using different bases, try practicing this important mathematical idea. The table below shows the number 459 broken down into three different bases. In each case, the 1s place is at the right, and the place values increase as you move to the left.

 

Why do you need a new symbol to represent the number 19 in base twenty? What other base-twenty numbers would you need to write with new symbols?
If you wrote “19” in base twenty, it would mean nine 1s and one 20 (which would be the number 29 in base ten).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In base twenty, every number less than 20 has to be written as a single digit in the 1s place. That’s easy for the numbers 1 to 9. We already have symbols for those. But what about the numbers 10 to 19? They’re two-digit numbers in base ten. So you’d have to create new symbols for all of them.
If you want more practice with different bases, choose two or three other numbers and write them in base twenty, base ten, and base five.