The question deals with the application of rounding rules in arithmetic operations, focusing on significant figures and decimal places. It covers when to round up or down and provides examples of adding, subtracting, multiplying, and dividing while retaining the correct precision.
The subject of the question is rounding numbers and performing arithmetic operations with careful attention to significant figures and decimal places. When adding or subtracting, the result should have the same number of decimal places as the original number with the fewest decimal places. For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures. Rounding errors can be minimized by retaining a guard digit during intermediate calculations or by combining calculations into a single step to avoid premature rounding.
For instance:
(a) 31.57 rounds "up" to 32 (the dropped digit is 5, and the retained digit is even)
(b) 8.1649 rounds "down" to 8.16 (the dropped digit, 4, is less than 5)
(c) 0.051065 rounds "down" to 0.05106 (the dropped digit is 5, and the retained digit is even)
(d) 0.90275 rounds "up" to 0.9028 (the dropped digit is 5, and the retained digit is even)
Here's a calculation example using a calculator:
If you calculate 337/217, you get 1.5529953917. If we were rounding to four decimal places as instructed, the result would be 1.5530.