A simple pendulum is made of a steel rod. If the temperature of the rod increases by 100 degrees Celsius, what is the percentage change in the time period of the pendulum?

The initial temperature is $T_1 = 25^\circ C$ and the final temperature is $T_2 = 125^\circ C$.
The change in temperature $\Delta T$ is:

$$\Delta T = T_2 - T_1 = 125^\circ C - 25^\circ C = 100^\circ C$$

The time period $T$ of a simple pendulum is given by:

$$T = 2\pi \sqrt{\frac{L}{g}}$$

where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity.

When the temperature changes, the length of the steel rod changes due to thermal expansion. The new length $L'$ is given by:

$$L' = L(1 + \alpha \Delta T)$$

where $\alpha$ is the coefficient of linear expansion for steel.

The new time period $T'$ will be:

$$T' = 2\pi \sqrt{\frac{L'}{g}} = 2\pi \sqrt{\frac{L(1 + \alpha \Delta T)}{g}} = T \sqrt{1 + \alpha \Delta T}$$

The fractional change in time period is $\frac{\Delta T_{period}}{T} = \frac{T' - T}{T} = \sqrt{1 + \alpha \Delta T} - 1$.
Since $\alpha \Delta T$ is very small, we can use the binomial approximation $(1+x)^n \approx 1+nx$ for small $x$. Here, $x = \alpha \Delta T$ and $n = \frac{1}{2}$.

$$\sqrt{1 + \alpha \Delta T} \approx 1 + \frac{1}{2} \alpha \Delta T$$

So, the fractional change in time period is approximately:

$$\frac{\Delta T_{period}}{T} \approx \left(1 + \frac{1}{2} \alpha \Delta T\right) - 1 = \frac{1}{2} \alpha \Delta T$$

The percentage change in time period is:

$$\text{Percentage change} = \frac{1}{2} \alpha \Delta T \times 100\%$$

Given $\alpha_{steel} = 1.2 \times 10^{-5} /^\circ C$ and $\Delta T = 100^\circ C$.

$$\text{Percentage change} = \frac{1}{2} \times (1.2 \times 10^{-5} /^\circ C) \times (100^\circ C) \times 100\%$$ $$\text{Percentage change} = 0.6 \times 10^{-5} \times 100 \times 100\%$$ $$\text{Percentage change} = 0.6 \times 10^{-5} \times 10^4 \%$$ $$\text{Percentage change} = 0.6 \times 10^{-1} \%$$ $$\text{Percentage change} = 0.06 \%$$

Since the temperature increases, the length of the pendulum increases, which leads to an increase in the time period. Therefore, the change is positive.

The final answer is \text{0.06%}.