I would like to convert my polygon data into a raster file to change the pixel resolution and then would like to convert it back to polygon data since this will allow it to be resampled to another resolution. The issue I face is that in the original polygon data that I convert it contains decimals like 1.87, I convert this field into a raster then when I convert this back to vector the values given are integers such as 2. How do I make sure the decimals are retained?
If the values are not preserved as decimals, you can recreate them in the polygonized layer by adding a new attribute with field calculater and get the raster-value of a point inside the polygon using this expression:
raster_value( 'name_of_your_raster_layer', 1, point_on_surface($geometry))
1 by the number of the raster layer's band from which you want to get the pixel value.
You don't say how you converted your polygon data to raster, but if you use the QGIS Raster > Conversion > Rasterize (Vector to Raster) tool it has the option to output the raster as a Float32 data type, which contains decimal places. Thus, your 1.87 will not be rounded to an integer value.
The tool also has the option to select which polygon field you wish to use as the output raster value. In my example below, that field is acres.
Having said this, your situation may contain a more important underlying question: should you be doing your analysis using all raster data, or all polygon data, instead of jumping back and forth between polygon and raster? That topic is out of scope for this question, but I would urge you to settle on one data type. Which data type you decide depends on the analysis you intend to conduct.