Question

we must take the uncertainty in our 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. rounding numbers 1. round 126.7892 to 3 significant figures: 127 2. round 0.007056 to 2 significant figures: 0.0071 3. round 5090 to 2 significant figures: 4. round 0.90997 to 4 significant figures: 5. round 8.00012 to 4 significant figures: 6. round 7500.89 to 2 significant figures: 7. round 0.00009875 to 3 significant figures: 8. round 57.567 to 3 significant figures: 9. round 4321 to 1 significant figure: 10. round 0.00556789 to 4 significant figures:

Explanation:

Step1: Identify significant - figure rules

For rounding to a certain number of significant figures, we follow the standard rules.

Step2: Round 5090 to 2 significant figures

The first two significant figures are 50. The next digit is 9 which is greater than 5, so we round up. 5090 rounds to 5100.

Step3: Round 0.90997 to 4 significant figures

The first four significant figures are 0.9099. The next digit is 7 which is greater than 5, so we round up. 0.90997 rounds to 0.9100.

Step4: Round 8.00012 to 4 significant figures

The first four significant figures are 8.000. The next digit is 1 which is less than 5, so we leave the retained digits as they are. 8.00012 rounds to 8.000.

Step5: Round 7500.89 to 2 significant figures

The first two significant figures are 75. The next digit is 0 which is less than 5, so we leave the retained digits as they are. 7500.89 rounds to 7500.

Step6: Round 0.00009875 to 3 significant figures

The first three significant figures are 0.0000987. The next digit is 5. Since the last non - zero digit in the retained part (7) is odd, we round up. 0.00009875 rounds to 0.0000988.

Step7: Round 57.567 to 3 significant figures

The first three significant figures are 57.5. The next digit is 6 which is greater than 5, so we round up. 57.567 rounds to 57.6.

Step8: Round 4321 to 1 significant figure

The first significant figure is 4. The next digit is 3 which is less than 5, so we leave the retained digit as it is. 4321 rounds to 4000.

Step9: Round 0.00556789 to 4 significant figures

The first four significant figures are 0.005567. The next digit is 8 which is greater than 5, so we round up. 0.00556789 rounds to 0.005568.

Answer:

1. 5100
2. 0.9100
3. 8.000
4. 7500
5. 0.0000988
6. 57.6
7. 4000
8. 0.005568