Question

we must take the uncertainty in our __________ into account to avoid misrepresenting the uncertainty in calculated results. one way to do this is to report the result of a calculation with the correct number of significant figures, which is determined by the following four rules for rounding numbers: when we ________ or ________ numbers, we should round the result to the same number of decimal places as the number with the least number of decimal places (the least uncertain value in terms of ________ and ________). when we ________ or ________ numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least uncertain value in terms of ________ and ________). if the digit to be dropped (the one immediately to the right of the digit to be retained) is less than 5, we “round down” and leave the retained digit ________; if it is more than 5, we “round up” and __________ the retained digit by 1; note: if the dropped digit is 5, and it’s either the last digit in the number or it’s followed only by zeros, round up or down, whichever yields an even value for the retained digit. if any nonzero digits follow the dropped 5, round up.

Explanation:

When dealing with measurements and calculations, we consider measurement uncertainty. For addition and subtraction of numbers, we round to the least - precise decimal place in terms of measurement precision and uncertainty. For multiplication and division, we round to the least number of significant figures considering precision and uncertainty. When rounding, if the digit to drop is less than 5, we keep the retained digit unchanged; if greater than 5, we increment the retained digit by 1.

Answer:

We must take the uncertainty in our measurements into account to avoid misrepresenting the uncertainty in calculated results. One way to do this is to report the result of a calculation with the correct number of significant figures, which is determined by the following four rules for rounding numbers:
When we add or subtract numbers, we should round the result to the same number of decimal places as the number with the least number of decimal places (the least uncertain value in terms of measurement precision and uncertainty).
When we multiply or divide numbers, we should round the result to the same number of digits as the number with the least number of significant figures (the least uncertain value in terms of precision and uncertainty).
If the digit to be dropped (the one immediately to the right of the digit to be retained) is less than 5, we “round down” and leave the retained digit unchanged; if it is more than 5, we “round up” and increase the retained digit by 1;
Note: If the dropped digit is 5, and it’s either the last digit in the number or it’s followed only by zeros, round up or down, whichever yields an even value for the retained digit. If any nonzero digits follow the dropped 5, round up.