When performing calculations, round off numbers after a few decimal places in your final answer (at the last step).

Consider the problem of stacking a set of bricks to equal the height of a wall (not a very astronomical problem, but one that is easy to visualize!). If the wall is 9.1 feet high, and an individual brick is 0.58 feet tall, how many bricks will it take to equal the height of the wall?

We calculate an answer by dividing the height of the wall by the height of a single brick.

N = 9.1 ÷ 0.58 = 15.689655

But is our answer really as precise as this? Do we know it this well? Are all of those numbers listed after the decimal place really telling us anything useful?

We must consider the accuracy of our measurements. We know that the height of the wall is measured to be 9.1 feet, which is is not the same as 9.10000000 feet. This tells us that the wall could be as high as 9.14 feet, or as low as 9.05 feet. (Why?) Similarly, the height of an individual brick is 0.58 feet, so an individual brick could be as tall as 0.584 feet or as short as 0.575 feet.

We calculate first the maximum number of bricks we might need. We will need the most bricks if the wall is highest, and the bricks are each as short as possible.

N = 9.14 ÷ 0.575 = 15.9

We calculate next the minimum number of bricks we might need. We will need the most bricks if the wall is lowest, and the bricks are each as tall as possible.

N = 9.05 ÷ 0.584 = 15.5

This tells us that our answer lies somewhere between 15.5 and 15.9. We won't know exactly where unless we remeasure the height of the wall and the bricks to a greater accuracy. Our final answer should reflect the accuracy of our initial measurements, and provide only as many decimal places as are useful.

N = 9.1 ÷ 0.58 = 15.7