Final answer:
Rounding rules require looking at the digit to the immediate right of the intended significant figure. If this digit is less than 5, the value is rounded down; if it's 5 or greater, round up, and when a 5 is followed by zeros or non-zero digits, round to the nearest even digit to avoid bias. These guidelines ensure accurate rounding during mathematical operations.
Step-by-step explanation:
When dealing with rounding numbers, it is important to understand the rules for determining the number of significant figures. Rounding to the nearest whole number involves looking at the digit immediately to the right of the decimal point. If this digit is less than 5, you round down, keeping the digit on the left unchanged. If it is 5 or greater, you round up, increasing the left-side digit by 1. In the case of a 5 followed by either zeros or no further digits, round to the nearest even digit to avoid bias.
Let's look at specific examples illustrating these rules:
- Number 0.028675 rounds up to 0.0287 because the dropped digit is 7, which is greater than 5.
- Number 18.3384 rounds down to 18.3 because the dropped digit is 3, which is less than 5.
- Number 6.8752 rounds up to 6.88 since the dropped digit is 5 and is followed by a nonzero digit.
- Number 92.85 rounds down to 92.8 because the dropped digit is 5 but the retained digit is even, adhering to the statistical rule to avoid bias with the digit 5.
It is crucial not to round off intermediate answers if multiple mathematical operations are being performed. This helps to ensure that the final result is as accurate as possible, rounding off only once at the end. During subtraction, it's important to round the result to the same number of significant figures present in the least precise measurement for accuracy.