A rectangular object has a length of (250 ± 1) mm and a width of (200 ± 1) mm. Calculate the fractional uncertainty in length and width, and the percentage error in length.

The fractional uncertainty is given by $\frac{\Delta L}{L_0}$.

$$\text{Fractional uncertainty in length} = \frac{1 \text{ mm}}{250 \text{ mm}}$$ $$\text{Fractional uncertainty in length} = 0.004$$

The fractional uncertainty in its length is $\boxed{0.004}$.

The fractional uncertainty is given by $\frac{\Delta W}{W_0}$.

$$\text{Fractional uncertainty in width} = \frac{1 \text{ mm}}{200 \text{ mm}}$$ $$\text{Fractional uncertainty in width} = 0.005$$

The fractional uncertainty in its width is $\boxed{0.005}$.

The percentage error is the fractional uncertainty multiplied by $100\%$.

$$\text{Percentage error in length} = \frac{\Delta L}{L_0} \times 100\%$$ $$\text{Percentage error in length} = 0.004 \times 100\%$$ $$\text{Percentage error in length} = 0.4\%$$

The percentage error on its length is $\boxed{0.4\%}$.

$$\text{Percentage error in width} = \frac{\Delta W}{W_0} \times 100\%$$ $$\text{Percentage error in width} = 0.005 \times 100\%$$ $$\text{Percentage error in width} = 0.5\%$$

The percentage error on its width is $\boxed{0.5\%}$.

The area of one side of the book is $A = L \times W$.

$$A_0 = L_0 \times W_0$$ $$A_0 = 250 \text{ mm} \times 200 \text{ mm}$$ $$A_0 = 50000 \text{ mm}^2$$

For multiplication, the fractional uncertainties add up:

$$\frac{\Delta A}{A_0} = \frac{\Delta L}{L_0} + \frac{\Delta W}{W_0}$$ $$\frac{\Delta A}{A_0} = 0.004 + 0.005$$ $$\frac{\Delta A}{A_0} = 0.009$$

$$\Delta A = A_0 \times \left(\frac{\Delta A}{A_0}\right)$$ $$\Delta A = 50000 \text{ mm}^2 \times 0.009$$ $$\Delta A = 450 \text{ mm}^2$$

$$A = (A_0 \pm \Delta A)$$ $$A = (50000 \pm 450) \text{ mm}^2$$

The area of one side of the book is $\boxed{(50000 \pm 450) \text{ mm}^2}$.