Re: Decimal math bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg28802] Re: Decimal math bug?
• From: "Paul Lutus" <nospam at nosite.com>
• Date: Mon, 14 May 2001 01:32:55 -0400 (EDT)
• References: <9dlc20\$o1r@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Jim Freeze" <jim at freeze.org> wrote in message
news:9dlc20\$o1r at smc.vnet.net...
> On Sat, 12 May 2001, Steven M. Christensen wrote:
>
>
> This looks like a bug.
>
> This is Mathematica 4.1 (just purchased) on Linux.
>
> In[88]:=(.53+.9) - (1.43) == 0
> Out[88]:=False
> ---------^^^^^
>
> In[89]:=(.53+.9) - (.43+1.0)== 0
> Out[89]:=False
> ---------^^^^^
>
> In[100]:=(.53+.9) - (.43+0.8+0.2) == 0
> Out[100]:=False
> ----------^^^^^
>
> In[102]:=(.53+.9) - (.43+0.8+0.1 +0.1) == 0
> Out[102]:=True
> ----------^^^^
>
> The above results from some strange decimal math:
> In[67]:=Range[.53,4,.9]
> Out[103]:={0.53, 1.4300000000000002, 2.33, 3.23}
>
> where sometimes 1.4300000000000002 == 1.43 and sometimes
> it doesn't.
>
> It is really disconcerting to have that trailing 2.
>
> Can someone please explain what is going on here?

Yes, certainly.

First, computers perform arithmetic using binary numbers. What you see are
decimal conversions of those numbers. Sometimes a perfectly normal-looking
decimal number has no finite representation in binary:

0.1 in base 10 is the repeating series 0.00011001100110011001101... in base
2.

There are also numbers in binary that have no finite representation in
decimal.

So when you say "strange decimal math," this is not quite right. It's binary
math, and decimal display.

This is true for virtually all computers, all computer programs, everywhere,
all the time. You just have to know it and accommodate it. The best way to
accommodate it in Mathematica is to use integers where possible and use
ratios, not decimals, when integers are not possible. This has the added
advantage that Mathematica's algebraic manipulations are more flexible.

> In[88]:=(.53+.9) - (1.43) == 0
> Out[88]:=False

Second, your example is wrong. 53 + 9 = 62, not 143. 53 + 9 - 62 == 0
always, not sometimes.

--
Paul Lutus
www.arachnoid.com

```

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