A student performs an experiment to determine the Young's modulus of a wire, exactly $2\,\text{m}$ long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be $0.80\,\text{mm}$ with an uncertainty of $\pm 0.05\,\text{mm}$ at a load of exactly $1.0\,\text{kg}$. The student also measures the diameter of the wire to be $0.4\,\text{mm}$ with an uncertainty of $\pm 0.01\,\text{mm}$. Take $g = 9.8\,\text{m/s}^2$ (exact). The Young's modulus obtained from the reading is