In a screw gauge there are 100 divisions on the circular scale and the main scale moves by 0.5mm on a complete rotation of the circular. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while ${46}^{\mathrm{th}}$ division the circular scale coincides with the reference line. The diameter of the wire is______  ${10}^{-2}\mathrm{mm}$