ArcToolbox has an option that allows you to export data in single or double precision. It could be possible that this option is set to export data in single precision.
Export tools in ArcCatalog are the same export tools provided in ArcToolbox.
- Start ArcToolbox.
- Select Tools > Options menu and click the Precision tab.
- Select Double precision for creating new data and click OK.
- Exit ArcToolbox.
- If ArcCatalog is running, exit and start a new ArcCatalog session.
- Right-click on a shapefile. Select Export > Shapefile to Coverage.
The exported data should result in double precision.