Multply polygon with raster

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I have a countries' polygon with an attribute table. I also have a raster. I want to multiply the values of the polygon (of each country) with the raster.

My idea was to convert the polygon to raster and use the value I want to multiply with the raster. However, the raster comes with 0 to 255 values and not with the ones I have on the attribute table.



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