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

### Base 5

```
Date: 07/28/97 at 21:28:42
From: Renee Jones
Subject: Bases

I am an Elementary Education major and was asked by my professor to
find out what .23 was in base 5. I am familiar with different bases
and I know that 6 in base 5 is 11, 7 is 12 and so on. Seeing how .23
is less than 1, would it be the same in base 5 as it is in base 10?
```

```
Date: 07/29/97 at 07:19:47
From: Doctor Anthony
Subject: Re: Bases

Just as .23 means  2/10 + 3/100, so when we express a number less than
1 in base 5, say the number .342 (base 5), we mean 3/5 + 4/25 + 2/125.

If we let  .23 = a/5 + b/25 + c/125  then multiplying both sides by 5

1.15 = a + b/5 + c/25  equate integer parts, so a = 1

.15 = b/5 + c/25      multiply again by 5

0.75 = b + c/5         equating integer parts b = 0

.75 = c/5             multiply by 5

3.75 = c + d/5         equating integer parts c = 3

.75 = d/5             multiply by 5

3.75 = d + e/5         equating integer parts d = 3

And so on.  Thus .23 (base 10) = .10333... (base 5)

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics: