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I've classified an elevation raster into 4 classes. Is there a way to export these class values (0, 1, 2, 3) to a separate raster? I've tried exporting the raster to file, but this just gives the same elevation values.

In other words, I want to replace the pixel values in my DEM with their class values.

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    This is what the Con (Spatial Analyst) tool was designed for. – Aaron Aug 13 '14 at 18:17
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Answered as How to perform Raster Reclassification in QGIS? indirectly, but I found it can be done either using the Con (Spatial Analyst) tool (@Aaron), or better using the Reclassify (Spatial Analyst) tool.

The "Classify..." button provides the same functionality as in the Layer Symbology dialogue box.

Reclassify creates a new raster based on the classification and Class Values.

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