Associated Topics || Dr. Math Home || Search Dr. Math

### Base 3

```
Date: 10/24/2001 at 11:09:42
From: Hannah Martin
Subject: Number systems (base 3)

What is 2+2 in base three?

I believe it to be 4 in any number system because a one-digit number
(x) in any base will be (x) times (the base to the zero power), or 1.

My teacher disagrees and says that she is sure that it isn't 4.
```

```
Date: 10/24/2001 at 12:17:58
From: Doctor Peterson
Subject: Re: Number systems (base 3)

Hi, Hannah.

You have to start by distinguishing a number from a numeral (a way of
writing a number). The sum 2+2 is always equal to the NUMBER 4; the
only question is how to WRITE this number in base 3. In base 3, you
count

1, 2, 10, 11, 12, 20, 21, ...

because "11" in base 3 means 1 three and 1 one.  This, therefore, is
how you write 4 in base 3. So the answer is, 11 (base 3).

The problem with saying that the answer is 4 is that, in base 3, there
is no symbol 4. Similarly, I could claim that in base ten, 6 + 6 = C,
because I am familiar with the base 16 system in which C is the digit
for twelve. To you, C is not a digit at all, so my answer is
meaningless to you - in base ten. I can't use C to write in base ten,
and you can't use 4 to write in base 3.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Number Sense/About Numbers
Middle School Number Sense/About Numbers

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search