Unfortunately, bc doesn’t support scientific notation.
However, it can be translated into a format that bc can handle, using extended regex as per POSIX in sed:
sed -E 's/([+-]?[0-9.]+)[eE]\+?(-?)([0-9]+)/(\1*10^\2\3)/g' <<<"$value"
you can replace the “e” (or “e+”, if the exponent is positive) with “*10^”, which bc will promptly understand. This works even if the exponent is negative or if the number is subsequently multiplied by another power, and allows keeping track of significant digits.
If you need to stick to basic regex (BRE), then this should be used:
sed 's/\([+-]\{0,1\}[0-9]*\.\{0,1\}[0-9]\{1,\}\)[eE]+\{0,1\}\(-\{0,1\}\)\([0-9]\{1,\}\)/(\1*10^\2\3)/g' <<<"$value"
From Comments:
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A simple bash pattern match could not work (thanks @mklement0) as there is no way to match a e+ and keep the – from a e- at the same time.
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A correctly working perl solution (thanks @mklement0)
$ perl -pe 's/([-\d.]+)e(?:\+|(-))?(\d+)/($1*10^$2$3)/gi' <<<"$value" -
Thanks to @jwpat7 and @Paul Tomblin for clarifying aspects of sed’s syntax, as well as @isaac and @mklement0 for improving the answer.
Edit:
The answer changed quite a bit over the years. The answer above is the latest iteration as of 17th May 2018. Previous attempts reported here were a solution in pure bash (by @ormaaj) and one in sed (by @me), that fail in at least some cases. I’ll keep them here just to make sense of the comments, which contain much nicer explanations of the intricacies of all this than this answer does.
value=${value/[eE]+*/*10^} ------> Can not work.
value=`echo ${value} | sed -e 's/[eE]+*/\\*10\\^/'` ------> Fail in some conditions