1. **Problem 6a:** Determine the number of significant figures in 0.004560. - Leading zeros are not significant. - The digits 4, 5, 6 are significant. - The trailing zero after 6 is significant because there is a decimal point. **Answer:** 4 significant figures. 2. **Problem 7a:** Round 0.00342678 to 4 significant figures. - The first four significant figures are 3, 4, 2, and 6. - The 7 following the 6 is considered for rounding. - Since 7 > 5, round up the last digit 6 to 7. **Rounded number:** 0.003427 3. **Problem 8:** Calculate and express the answer to 3 significant figures: $$ (6.14 \times 10^4) \times (2.1 \times 10^2) $$ - Multiply the coefficients: $6.14 \times 2.1 = 12.894$ - Add exponents: $10^4 \times 10^2 = 10^{4+2} = 10^6$ - So, product is $12.894 \times 10^6 = 1.2894 \times 10^7$ - Round to 3 significant figures: $1.29 \times 10^7$ 4. **Problem 9:** Calculate sum and round to 2 decimal places: $$43.62 + 0.0317 + 7.1 = 43.62 + 0.0317 + 7.1$$ - Sum: $43.62 + 0.0317 = 43.6517$ - Add 7.1: $43.6517 + 7.1 = 50.7517$ - Round to 2 decimal places: $50.75$ 5. **Problem 10:** Divide and round to 3 decimal places: $$123.45 \div 6.7$$ - Compute division: $123.45 \div 6.7 \approx 18.4179104$ - Round to 3 decimal places: $18.418$ **Final answers:** 6a) 4 significant figures 7a) 0.003427 8) $1.29 \times 10^7$ 9) 50.75 10) 18.418