Re: rounding

• To: mathgroup at smc.vnet.net
• Subject: [mg49526] Re: [mg49469] rounding
• From: Ramesh Raju Mudunuri <rmudunuri at uh.edu>
• Date: Thu, 22 Jul 2004 02:46:58 -0400 (EDT)
• References: <200407211039.GAA07808@smc.vnet.net>
• Reply-to: Ramesh Raju Mudunuri <rmudunuri at uh.edu>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
With a little modification, your code will do what you wanted. Due to
chopping and rounding errors your code does not work properly.
You can use

round[x_, y_] := (Round[x 10^y] 10^(-y)) // N

where we first rationalize and then ask for the numerical value. You get the
answer you are looking for through round[mylist,2]. A more elaborate way
would be to define
round2[x_?NumericQ,
y_Integer?NonNegative] := ((Round[x*(10^y)])(10^(-y)) // N) /; ! IntegerQ[x]
round2[x_?NumericQ, y_Integer?NonNegative] := x /; IntegerQ[x]

and use Map as in

Map[round2[#, 2] &, mylist]

to round mylist (Conditions have been used to define round2, to let integers
be as they are). Similar functions can be written to chop a real number to a
given number of decimals, where IntegerPart is used instead of Round.

Ramesh

----- Original Message -----
From: Amit Gandhi
To: mathgroup at smc.vnet.net
To: mathgroup at smc.vnet.net
Sent: Wednesday, July 21, 2004 5:39 AM
Subject: [mg49526] [mg49469] rounding

Hello Group:
I was wondering if anyone might be able to explain why mathematica
does the following -
In Mathematica I create a list of numbers as follows:

mylist - Table[i, {i, 1., 8., .2}];

This produces

{1., 1.2, 1.4, 1.6, 1.8, 2.05, 2.2, 2.4, 2.6, 2.8, 3., 3.2, 3.4,
3.6, 3.8, \ 4., 4.2, 4.4, 4.6, 4.8, 5., 5.2, 5.4, 5.6, 5.8, 6., 6.2,
6.4, 6.6, 6.8, 7., \ 7.2, 7.4, 7.6, 7.8, 8.}

However if I try editing this output, it shows me that the full form
of this list is:

{1.`, 1.2`, 1.4000000000000001`, 1.6`, 1.8`, 2.05`, 2.2`, 2.4`,
2.6`, \ 2.8000000000000003`, 3.`, 3.2`, 3.4`, 3.6`,
3.8000000000000003`, 4.`, 4.2`, \ 4.4`, 4.6000000000000005`, 4.8`,
5.`, 5.2`, 5.4`, 5.6000000000000005`, 5.8`, \ 6.`, 6.2`, 6.4`,
6.6000000000000005`, 6.8`, 7.`, 7.2`, 7.4`, \ 7.6000000000000005`,
7.8`, 8.`}

I would like this bottom list to be rounded so that the full form is
equivalent to the first list. So I wrote a round function that
rounds a real number to a specified number of decimal places:

round[x_, place_] := (Round[x*(10.^place)])/(10.^place);

so for instance round[3.456, 2] = 3.46.

Now when I do round[mylist, 2], the full form of the numbers in the
list continue to be

{1.`, 1.2`, 1.4000000000000001`, 1.6`, 1.8`, 2.05`, 2.2`, 2.4`,
2.6`, \ 2.8000000000000003`, 3.`, 3.2`, 3.4`, 3.6`,
3.8000000000000003`, 4.`, 4.2`, \ 4.4`, 4.6000000000000005`, 4.8`,
5.`, 5.2`, 5.4`, 5.6000000000000005`, 5.8`, \ 6.`, 6.2`, 6.4`,
6.6000000000000005`, 6.8`, 7.`, 7.2`, 7.4`, \ 7.6000000000000005`,
7.8`, 8.`}

Can anyone explain to me how to properly round numbers in mathematica.

--Boundary_(ID_hdYnexqwD6R1NGQI2YKgiw)

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
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<BODY bgColor=#ffffff>
<DIV><FONT face=Verdana size=2>Hi,</FONT></DIV>
<DIV><FONT face=Verdana size=2>With a little modification, your code will do
what you wanted. Due to </FONT></DIV>
<DIV><FONT face=Verdana size=2>chopping and rounding errors your code does not
work properly. </FONT></DIV>
<DIV><FONT face=Verdana size=2>You can use</FONT></DIV>
<DIV>&nbsp;</DIV>
<DIV>round[x_, y_] := (Round[x 10^y] 10^(-y)) // N</DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=Verdana size=2>where we first rationalize and then ask for the
numerical value. You get the</FONT></DIV>
<DIV><FONT face=Verdana size=2>answer you are looking for through
round[mylist,2]. A more elaborate way</FONT></DIV>
<DIV><FONT face=Verdana size=2>would be to define </FONT></DIV>
<P>round2[x_?NumericQ, <BR>y_Integer?NonNegative] := ((Round[x*(10^y)])(10^(-y))
// N) /; ! IntegerQ[x]<BR>round2[x_?NumericQ, y_Integer?NonNegative] := x /;
IntegerQ[x]</P>
<DIV>and use Map as in</DIV>
<DIV>&nbsp;</DIV>
<DIV>Map[round2[#, 2] &amp;, mylist] </DIV>
<DIV>&nbsp;</DIV>
<DIV><FONT face=Verdana size=2>to round mylist (Conditions have been used to
define round2, to let integers</FONT></DIV>
<DIV><FONT face=Verdana size=2>be as they are). </FONT><FONT face=Verdana
size=2>Similar functions can be written to chop a real number </FONT><FONT
face=Verdana size=2>to a </FONT></DIV>
<DIV><FONT face=Verdana size=2>given number of decimals, where IntegerPart is
<DIV><FONT face=Verdana size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Verdana size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Verdana size=2>Ramesh</FONT></DIV>
<DIV><FONT face=Verdana size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Verdana size=2></FONT>&nbsp;</DIV>
<DIV><FONT face=Verdana size=2></FONT>&nbsp;</DIV>
<BLOCKQUOTE
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
To: mathgroup at smc.vnet.net
<A title=akgandhi at uchicago.edu href="mailto:akgandhi at uchicago.edu">Amit
Gandhi</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=mathgroup at smc.vnet.net
href="mailto:mathgroup at smc.vnet.net">mathgroup at smc.vnet.net</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, July 21, 2004 5:39
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [mg49469] rounding</DIV>
<DIV><BR></DIV><BR><BR>Hello Group:<BR>I was wondering if anyone might be able
to explain why mathematica <BR>does the following -<BR>In Mathematica I create
a list of numbers as follows:<BR><BR>mylist - Table[i, {i, 1., 8.,
.2}];<BR><BR>This produces<BR><BR>{1., 1.2, 1.4, 1.6, 1.8, 2.05, 2.2, 2.4,
2.6, 2.8, 3., 3.2, 3.4, <BR>3.6, 3.8, \ 4., 4.2, 4.4, 4.6, 4.8, 5., 5.2, 5.4,
5.6, 5.8, 6., 6.2, <BR>6.4, 6.6, 6.8, 7., \ 7.2, 7.4, 7.6, 7.8,
8.}<BR><BR>However if I try editing this output, it shows me that the full
form <BR>of this list is:<BR><BR>{1.`, 1.2`, 1.4000000000000001`, 1.6`, 1.8`,
2.05`, 2.2`, 2.4`, <BR>2.6`, \ 2.8000000000000003`, 3.`, 3.2`, 3.4`, 3.6`,
<BR>3.8000000000000003`, 4.`, 4.2`, \ 4.4`, 4.6000000000000005`, 4.8`,
<BR>5.`, 5.2`, 5.4`, 5.6000000000000005`, 5.8`, \ 6.`, 6.2`, 6.4`,
<BR>6.6000000000000005`, 6.8`, 7.`, 7.2`, 7.4`, \ 7.6000000000000005`,
<BR>7.8`, 8.`}<BR><BR>I would like this bottom list to be rounded so that the
full form is <BR>equivalent to the first list. So I wrote a round function
that <BR>rounds a real number to a specified number of decimal
places:<BR><BR>round[x_, place_] :=
(Round[x*(10.^place)])/(10.^place);<BR><BR>so for instance round[3.456, 2] =
3.46.<BR><BR>Now when I do round[mylist, 2], the full form of the numbers in
the <BR>list continue to be<BR><BR>{1.`, 1.2`, 1.4000000000000001`, 1.6`,
1.8`, 2.05`, 2.2`, 2.4`, <BR>2.6`, \ 2.8000000000000003`, 3.`, 3.2`, 3.4`,
3.6`, <BR>3.8000000000000003`, 4.`, 4.2`, \ 4.4`, 4.6000000000000005`, 4.8`,
<BR>5.`, 5.2`, 5.4`, 5.6000000000000005`, 5.8`, \ 6.`, 6.2`, 6.4`,
<BR>6.6000000000000005`, 6.8`, 7.`, 7.2`, 7.4`, \ 7.6000000000000005`,
<BR>7.8`, 8.`}<BR><BR>Can anyone explain to me how to properly round numbers
in mathematica.<BR></BLOCKQUOTE></BODY></HTML>

--Boundary_(ID_hdYnexqwD6R1NGQI2YKgiw)--

```

• References:
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• From: Amit Gandhi <akgandhi@uchicago.edu>
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