In an experiment to determine the Young's modulus of wire of a length exactly $1 \mathrm{~m}$, the extension in the length of the wire is measured as $0.4 \mathrm{~mm}$ with an uncertainty of $\pm\, 0.02 \mathrm{~mm}$ when a load of $1 \mathrm{~kg}$ is applied. The diameter of the wire is measured as $0.4 \mathrm{~mm}$ with an uncertainty of $\pm \,0.01 \mathrm{~mm}$. The error in the measurement of Young's modulus $(\Delta \mathrm{Y})$ is found to be $x \times 10^{10}\, \mathrm{Nm}^{-2}$. The value of $x$ is $\underline{\hspace{2cm}}$. $$\left(\right.$$ take $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )