In a screw gauge, there are \(100\) divisions on the circular scale and the main scale moves by \(0.5 \, \text{mm}\) on a complete rotation of the circular scale. 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 \(46^{\text{th}}\) division the circular scale coincide with the reference line. The diameter of the wire is _______ \( \times 10^{-2} \, \text{mm} \).
