1. The question "when do we half the number" relates to situations where a quantity is reduced to half its original value. 2. This commonly appears in problems involving exponential decay, such as half-life in physics or biology. 3. For example, if the original number is $N_0$, we want to find the time $t$ when it becomes $\frac{N_0}{2}$. 4. In exponential decay, the relationship is $N = N_0 e^{-kt}$, where $k$ is the decay constant. 5. To half the number, set $N = \frac{N_0}{2}$: $$\frac{N_0}{2} = N_0 e^{-kt}$$. 6. Divide both sides by $N_0$: $$\frac{1}{2} = e^{-kt}$$. 7. Take natural logarithm of both sides: $$\ln \frac{1}{2} = -kt$$. 8. Solve for $t$: $$ t = \frac{\ln 2}{k} $$. 9. This $t$ is called the half-life, the time to reduce the number to half. 10. So, we half the number at time $t = \frac{\ln 2}{k}$ in exponential decay processes.