The end of a pier was destroyed during a storm.

Before the storm, the pier was $800 \mathrm{~m}$ long, rounded to 2 significant figures. The storm destroyed $200 \mathrm{~m}$ of the pier, rounded to 1 significant figure.

Work out the lower and upper bounds of the length of the pier after the storm. Give your answers in metres $(\mathrm{m})$.

Step 1 ：The pier was 800m long before the storm, rounded to 2 significant figures. This means the actual length of the pier could be anywhere from 795m to 805m.

Step 2 ：The storm destroyed 200m of the pier, rounded to 1 significant figure. This means the actual length destroyed could be anywhere from 150m to 250m.

Step 3 ：To find the lower and upper bounds of the length of the pier after the storm, we need to subtract the maximum and minimum possible lengths destroyed from the maximum and minimum possible lengths of the pier before the storm.

Step 4 ：lower_bound_before = 795

Step 5 ：upper_bound_before = 805

Step 6 ：lower_bound_destroyed = 150

Step 7 ：upper_bound_destroyed = 250

Step 8 ：lower_bound_after = lower_bound_before - upper_bound_destroyed = 795 - 250 = 545

Step 9 ：upper_bound_after = upper_bound_before - lower_bound_destroyed = 805 - 150 = 655

Step 10 ：Final Answer: The lower and upper bounds of the length of the pier after the storm are \(\boxed{545 \mathrm{~m}}\) and \(\boxed{655 \mathrm{~m}}\) respectively.