A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{b d}{D}=\mathrm{m} \lambda$, where b is the slit width, D the shortest distance between the slit and the screen, d the distance between the $\mathrm{m}_{\hat{\sim}}^{\text {th }}$ diffraction maximum and the central maximum, and $\lambda$ is the wavelength. D and d are measured with scales of least count of 1 cm and 1 mm , respectively. The values of $\lambda$ and m are known precisely to be 600 nm and 3, respectively. The absolute error (in $\mu \mathrm{m}$ ) in the value of b estimated using the diffraction maximum that occurs for $m=3$ with $d=5 \mathrm{~mm}$ and $D=1 \mathrm{~m}$ is $\_\_\_\_$