Using ReplaceAll (/.) on numerical digits

• To: mathgroup at smc.vnet.net
• Subject: [mg113253] Using ReplaceAll (/.) on numerical digits
• From: Richard Klopp <rklopp at exponent.com>
• Date: Wed, 20 Oct 2010 04:10:37 -0400 (EDT)

```Background:
I made some lab measurements and then calibrated the test instrument after
the fact. This changed the measurements slightly. I wanted to replace the
measurements with the calibrated values. The measurements were all very
close to 0.5600, only differing in the thousandths and ten-thousandths
places, so I coded my original data as a list of two-digit integers
{20,30,40}, then divided the whole list by 10000 and added 0.5600 to it.

I found some seemingly weird behavior with ReplaceAll as shown below. Note
how 0.563 in data remains untouched while 0.562 and 0.564 get replaced as
intended, but when I simply type in 0.563 and do a replace, it gets replaced
successfully. Can someone explain why this happens?

In any event, I've got a workaround based on StringReplace, which is likely
safer whether the weird behavior is a bug or a misunderstanding on my part.

data = 0.5600 + 1/10000 {20, 30, 40} {0.562, 0.563, 0.564} (* 0.563 stays
untouched *) data /. {0.562 -> 0.5622, 0.563 -> 0.5637, 0.564 -> 0.5641}
{0.5622, 0.563, 0.5641} (* 0.563 stays untouched *) (0.5600 + 1/10000 {20,
30, 40}) /. {0.562 -> 0.5622, 0.563 -> 0.5637,   0.564 -> 0.5641} {0.5622,
0.563, 0.5641} (* 0.563 stays untouched *) {0.5600 + 20/10000, 0.5600 +
30/10000,   0.5600 + 40/10000} /. {0.562 -> 0.5622, 0.563 -> 0.5637,   0.564
-> 0.5641} {0.5622, 0.563, 0.5641} (* 0.563 gets replaced when typed in
directly *) {0.562, 0.563, 0.564, 0.5630} /. {0.562 -> 0.5622, 0.563 ->
0.5637,   0.564 -> 0.5641} {0.5622, 0.5637, 0.5641, 0.5637}

(*workaround*) replaceDigits[numList_List, replacementDigitsList_List] := ToExpression[  StringReplace[   ToString[PaddedForm[#, {5, 5}] & /@
numList],    Map[ToString[PaddedForm[#, {5, 5}]] &, replacementDigitsList,
{2}]   ]  ] replaceDigits[data, {0.562 -> 0.5622, 0.563 -> 0.5637,   0.564
-> 0.5641}] {0.5622, 0.5637, 0.5641}

```

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