Units And Measurements

The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young’s modulus is $\alpha \times 10^9 \ \mathrm{N/m}^2$. The value of $\alpha$ is ________.

(Ignore the contribution of the load to Young’s modulus error calculation)