Express each result to the correct # of significant figures
1. 8.27 x (4.987 - 4.96)
2. (9.5 + 4.1 +2.8 +3.175)/4
3. (9.125 - 9.02) / 9.125 x 100
1. First, subtract 4.96 from 4.987. The result is 0.027.
Now, multiply 8.27 by 0.027. The result is 0.22269.
Since 8.27 has three significant figures, we need to round our answer to three significant figures as well.
Therefore, the result is 0.223.
2. Add 9.5, 4.1, 2.8, and 3.175 together. The sum is 19.575.
Divide 19.575 by 4. The result is 4.89375.
Since 9.5, 4.1, 2.8, and 3.175 all have two significant figures, we need to round our answer to two significant figures as well.
Therefore, the result is 4.9.
3. First, subtract 9.02 from 9.125. The result is 0.105.
Now, multiply 0.105 by 100. The result is 10.5.
Since 9.125 has four significant figures, we need to round our answer to four significant figures as well.
Therefore, the result is 10.50.
To express each result to the correct number of significant figures, we need to follow a few rules:
1. For addition and subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places.
2. For multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures.
Let's apply these rules to solve each problem:
1. 8.27 x (4.987 - 4.96):
- Subtracting 4.987 - 4.96 = 0.027.
- Multiplying 8.27 by 0.027 = 0.22329.
- The measurement with the fewest significant figures is 8.27, which has three significant figures.
- Therefore, expressing the result to the correct number of significant figures is 0.223.
2. (9.5 + 4.1 + 2.8 + 3.175) / 4:
- Adding 9.5 + 4.1 + 2.8 + 3.175 = 19.575.
- Dividing 19.575 by 4 = 4.89375.
- The measurement with the fewest significant figures is 4.1, which has two significant figures.
- Therefore, expressing the result to the correct number of significant figures is 4.9.
3. (9.125 - 9.02) / 9.125 x 100:
- Subtracting 9.125 - 9.02 = 0.105.
- Dividing 0.105 by 9.125 = 0.011506849315068493.
- Multiplying by 100 = 1.1506849315068493.
- The measurement with the fewest significant figures is 9.02, which has three significant figures.
- Therefore, expressing the result to the correct number of significant figures is 1.15.