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Significant Figures

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Significant Figures


**Task:** Answer questions on significant figures and scientific notation. 1. **What are significant figures?** Options: A, B, C, D Significant figures are the first non-zero digit and all digits that follow in a number. Answer: C 2. **How many significant figures are in 0.00564?** Leading zeros do not count. Count digits: 5, 6, 4 → 3 significant figures. Answer: B 3. **In 7.502, which digit is least significant?** The least significant digit is the one farthest to the right: 2. Answer: D 4. **Which number has 4 significant figures?** A) 0.0120 → 3 digits (1,2,0) B) 1200 → ambiguous but usually 2 unless specified C) 0.00012 → 2 digits D) 120.0 → counts trailing zero; 4 digits Answer: D 5. **Convert 3.25 x 10^4 to standard form:** Multiply: $3.25 \times 10^{4} = 32500$ Answer: C 6. **Significant figures in 700040?** Without decimal point, trailing zeros ambiguous. Here, likely 5 significant figures (7,0,0,0,4,0 → last zero ambiguous but if not decimal, omit last zero) Assuming trailing zero significant, answer: C (5) 7. **Standard form of 5.6 x 10^-3:** $5.6 \times 10^{-3} = 0.0056$ Answer: B 8. **Round 7.452 + 3.18 to 3 significant figures:** Sum: $7.452 + 3.18 = 10.632$ Rounded to 3 significant figures: 10.6 (since 10.6 has 3 sig figs: 1,0,6) Answer: A 9. **Convert 9.75 x 10^-2 to standard form:** $9.75 \times 10^{-2} = 0.0975$ Answer: A 10. **Product of 2.3 x 10^3 and 1.5 x 10^-2:** Multiply: $$2.3 \times 10^{3} \times 1.5 \times 10^{-2} = 2.3 \times 1.5 \times 10^{3 + (-2)} = 3.45 \times 10^{1}$$ Standard form: $3.45 \times 10^{1} = 34.5$ Among options, match is 34.5 x 10^-3 (which is 0.0345, incorrect), 3.45 x 10^-5 (too small), 345 x 10^-4 ( = 0.0345), 3.45 x 10^4 (too large). None matches exactly, but correct scientific notation is $3.45 \times 10^{1}$. Given options discrepancy, closest is none strictly correct, but best matching standard form is 34.5 (needs no exponent). So answer matches none exactly. Possibly misprint. **Final answers:** 1:C 2:B 3:D 4:D 5:C 6:C 7:B 8:A 9:A 10: None exactly, exact is $3.45 \times 10^{1}$ (not among options)