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What is the most elegant way to convert arbitrary numbers written as (verbatim):

1.13903 e - 08

into traditional Mathematica number form without having to convert the number into text (string), performing text substitutions, and so on?

(Of course 1.13903 e - 08 is $1.13903 \cdot 10^{-8}$.)

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3 Answers 3

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Closest to sensible I can imagine would be wrapping these numbers individually with a function if e is always followed by sign (+or -):

ClearAll@fn;
fn[m_. e + e_] := m 10^e;
fn[m_. e] := m;
fn[_] := 0;

fn[1.13903 e - 08]

1.13903*10^-8

Handling the case where + is implicit seems awfully convoluted to get right.

I also thought of redefining e as an operator, but firstly I don't think arbitrary letters can be redefined that way, and secondly all hell would probably break loose if such a definition would be present globally.

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    $\begingroup$ Yes... this works, and certainly along my initial efforts. Thanks. I was hoping for some clever option for NumberForm but this will do. ($\checkmark$) $\endgroup$
    – David G. Stork
    Commented May 7, 2020 at 5:50
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    $\begingroup$ But it actually works in this form only if your have + or - after e! I'll try to work a little more on it. $\endgroup$
    – kirma
    Commented May 7, 2020 at 5:52
  • $\begingroup$ HoldAll will help you handling 4 e 5 :) . $\endgroup$
    – xzczd ♦
    Commented May 7, 2020 at 6:53
  • $\begingroup$ @xzczd I tried it and failed to make it work in a sensible manner. Probably worth a second answer. In particular, ordering changes seem to occur depending on values of mantissa and exponent. $\endgroup$
    – kirma
    Commented May 7, 2020 at 6:55
  • $\begingroup$ That should not happen. Orderless doesn't start up in a function with HoldAll attribute. See my answer for more info. $\endgroup$
    – xzczd ♦
    Commented May 7, 2020 at 7:04
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An enhanced version of kirma's answer, which handles expressions like 5 e 4:

ClearAll@fn;
SetAttributes[fn, HoldAll]
fn[m_. e + e_] := m 10^e
fn[a_. e b_] := a 10^b

fn[5 e 4]
(* 50000 *)
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    $\begingroup$ Hah! I tested my function... having wrong definition overriding the one I was attempting to test in the front of tests being run. Now I understand why it didn't work. :) $\endgroup$
    – kirma
    Commented May 7, 2020 at 7:06
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you are fighting with windmills.

   Interpreter["Number"]["4.5E-7"]

gives you 4.5*10^-7

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    $\begingroup$ But OP mentions that he doesn't want to "convert the number into text (string)". And for that case, I'll use Internal`StringToDouble. $\endgroup$
    – xzczd ♦
    Commented May 7, 2020 at 7:57
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    $\begingroup$ @xzczd, How can you import arbitrary number to MMa? I know two ways - read from file and from shared memory. Both of them mean interpretation of textual or binary data. However, the form like xxE-yy is direct pointer to the textual data isn't it? $\endgroup$
    – Rom38
    Commented May 7, 2020 at 8:02
  • $\begingroup$ One possibility is, OP just want to type numbers using the e notation. Similar question comes up before: mathematica.stackexchange.com/q/135867/1871 $\endgroup$
    – xzczd ♦
    Commented May 7, 2020 at 8:08
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    $\begingroup$ But Interpreter["Number"]["1.13903 e - 08"] returns a Failure. $\endgroup$
    – corey979
    Commented May 7, 2020 at 8:28
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    $\begingroup$ @DavidG.Stork: Even then, the most practical solution is probably Interpreter["Number"][StringDelete["1.13903 e - 08", " "]], even if it does technically "perform a text substitution". $\endgroup$
    – Ilmari Karonen
    Commented May 8, 2020 at 12:39

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