The multiple reclassify tools in the spatial analyst toolbox (Reclass, Lookup, Reclass by ASCII file, Reclass by table) do not support a floating point output raster. It would be great if this can be implemented.
The present workaround I follow is to multiply the required floating point numbers by a large number, run the reclass tools to create an integer output and then use the divide tool to get the required floating point raster.
Have you tried the Remap raster function?
It allows you to give a range of values (min and max) and then the output value.
(Since it is a raster function, it is a virtual\in-memory layer. So if you want to persist it, you can use Export Raster to save it to a file. )
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