Question

Carry out the following operations, and express the answers with the appropriate number of significant figures. (a) \(12.0550+9.05\) (b) \(257.2-19.789\) (c) \(\left(6.21 \times 10^{3}\right)(0.1050)\) (d) \(0.0577 / 0.753\)

Short answer

(a) \(21.11\), (b) \(237.4\), (c) \(652\), (d) \(0.0766\)

Step-by-step solution

(a) Addition

To perform addition with significant figures, follow these steps: 1. Align the numbers according to the decimal places. 2. Add the numbers as usual. 3. Round the final answer to the least number of decimal places present in any of the numbers being added. For \(12.0550 + 9.05\), we first align the numbers and then add them: ``` 12.0550 + 9.05 ``` After adding, we get \(21.1050\). In the given numbers, 9.05 has the least decimal places (2 decimal places). Thus, we round the answer to 2 decimal places: Answer: \(21.11\)

(b) Subtraction

To perform subtraction with significant figures, follow these steps: 1. Align the numbers according to the decimal places. 2. Subtract the numbers as usual. 3. Round the final answer to the least number of decimal places present in any of the numbers being subtracted. For \(257.2 - 19.789\), we first align the numbers and then subtract them: ``` 257.200 - 19.789 ``` After subtracting, we get \(237.411\). In the given numbers, 257.2 has the least decimal places (1 decimal place). Thus, we round the answer to 1 decimal place: Answer: \(237.4\)

(c) Multiplication

To perform multiplication with significant figures, follow these steps: 1. Multiply the numbers as usual, ignoring the number of decimal places. 2. Round the final answer to the least number of significant figures present in any of the numbers being multiplied. For \((6.21 \times 10^{3}) (0.1050)\), we first multiply the numbers: \(6.21 \times 10^{3} \times 0.1050 = 652.3050\) In the given numbers, 6.21 has the least number of significant figures (3 significant figures). Thus, we round the answer to 3 significant figures: Answer: \(652\)

(d) Division

To perform division with significant figures, follow these steps: 1. Divide the numbers as usual, ignoring the number of decimal places. 2. Round the final answer to the least number of significant figures present in any of the numbers being divided. For \(\frac{0.0577}{0.753}\), we first divide the numbers: \(0.0577 \div 0.753 \approx 0.076606\) In the given numbers, 0.0577 has the least number of significant figures (3 significant figures). Thus, we round the answer to 3 significant figures: Answer: \(0.0766\)