A steel measuring tape gives correct readings at $20^\circ\text{C}$. On a day when the temperature is $40^\circ\text{C}$, it is used to measure a rod, and the reading is exactly $10.000\ \text{m}$. The coefficient of linear expansion of steel is $1.2 \times 10^{-5}\ \text{K}^{-1}$, and the rod is made of a material that hardly expands. Compared with the reading, the true length of the rod is