Final answer:
The correct equation for rounding a to three decimal places and b to four decimal places is a = round(a, 3) and b = round(b, 4).
Step-by-step explanation:
The correct equation with a rounded value of a to three decimal places and b to four decimal places is given by a = round(a, 3) and b = round(b, 4). Rounding off a decimal number is done by counting the number of decimal places you want to keep, and then determining whether to round up or down based on the digit immediately following your cutoff point. If this digit is 5 or higher, you round up. Otherwise, you round down.
When applying rules of rounding:
- For addition and subtraction, round the result to the same number of decimal places as the number with the least decimal places involved in the operation.
- For multiplication and division, round the result to the same number of significant figures as the original number with the least number of significant figures.
As an example, consider two numbers involved in a calculation - one represented by a and the other by b. If we need to round the value of a to three decimal places and the value of b to four decimal places, the correct equations would be a = round(a, 3) and b = round(b, 4). This ensures that a has 3 digits after the decimal while b has 4 digits after the decimal, once rounded accordingly.