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Counting in Base 5

Date: 03/02/2004 at 09:25:55
From: NaTasha
Subject: I need help

There are 5 counting numerals in base 5 (0 to 4).  Count from 1 to 7 
in base 5.  I just don't understand to do it.

Date: 03/02/2004 at 11:09:29
From: Doctor Peterson
Subject: Re: I need help

Hi, NaTasha.

In base 5, you count by fives the way we count by tens in base ten.

Here's how you count in base 10:

   o                1
   oo               2
   ooo              3
   oooo             4
   ooooo            5
   oooooo           6
   ooooooo          7
   oooooooo         8
   ooooooooo        9
  [oooooooooo]     10 = 1 ten and 0
  [oooooooooo] o   11 = 1 ten and 1
  [oooooooooo] oo  12 = 1 ten and 2

Once you reach ten, you start counting groups of ten, with extra ones 
left over.

In base 4, to use a different example, we group by 4's:

   o                1
   oo               2
   ooo              3
  [oooo]           10 = 1 four and 0   (this is 4 in base ten)
  [oooo] o         11 = 1 four and 1   (this is 5 in base ten)
  [oooo] oo        12 = 1 four and 2   (this is 6 in base ten)
  [oooo] ooo       13 = 1 four and 3   (this is 7 in base ten)
  [oooo][oooo]     20 = 2 fours and 0  (this is 8 in base ten)
  [oooo][oooo] o   21 = 2 fours and 1  (this is 9 in base ten)

So each time you have a new complete group of four, you add 1 to the
"fours" place, and start over with 0 ones.  We never have more than 3
in any place in the number, since if there were four or more we could
package them up.

Can you try the same thing with base 5?

Here is a place to look for more help:

  Number bases 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum 
Associated Topics:
High School Number Theory
Middle School Number Sense/About Numbers

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