This might be close, using Perl:
perl -pe 's/([+-]?[0-9.]+)/$1*19.123456789123/ge' YourFile
Sample Output
-4894.92001617493
-4894.96925301402
-4914.3031850202
-4952.55012214707
-4971.67357651707
That kind of says... "capture anything that starts with an optional plus or minus and has a bunch digits and decimal points and call it capture group 1. Replace that with whatever it was multiplied by your magic number. The e
at the end, says to evaluate the right side as an expression rather than take it as a literal. The g
at the end says to do it each and every time it occurs on each line, rather than just the first time."
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