1. **State the problem:** Determine if the given numbers are correctly written in scientific notation and write numbers in scientific notation or standard form as requested. 2. **Scientific notation rules:** A number in scientific notation is written as $$a \times 10^n$$ where $$1 \leq |a| < 10$$ and $$n$$ is an integer. 3. **Check each given number for correct scientific notation:** - 1) $$71 \times 10^{-2}$$: Here, $$a=71$$ which is not between 1 and 10, so **incorrect**. - 2) $$8 \times 10^{-2}$$: $$a=8$$ is between 1 and 10, so **correct**. - 3) $$0.99 \times 10^{-3}$$: $$a=0.99$$ is less than 1, so **incorrect**. - 4) $$1.2 \times 10^{4}$$: $$a=1.2$$ is between 1 and 10, so **correct**. 4. **Write numbers in scientific notation:** - 5) 533,000 = $$5.33 \times 10^{5}$$ (move decimal 5 places left) - 6) 327.8 = $$3.278 \times 10^{2}$$ (move decimal 2 places left) - 7) 0.0034 = $$3.4 \times 10^{-3}$$ (move decimal 3 places right) - 8) 0.00000728 = $$7.28 \times 10^{-6}$$ (move decimal 6 places right) 5. **Write numbers in standard form:** - 9) $$7.36 \times 10^{3} = 7360$$ (move decimal 3 places right) - 10) $$2.431 \times 10^{4} = 24310$$ (move decimal 4 places right) - 11) $$5.27 \times 10^{-2} = 0.0527$$ (move decimal 2 places left) - 12) $$4.01 \times 10^{-4} = 0.000401$$ (move decimal 4 places left) 6. **Identify the lesser number in each pair:** - 13) $$8.7 \times 10^{6} = 8,700,000$$ and $$5.9 \times 10^{3} = 5,900$$; lesser is $$5.9 \times 10^{3}$$ - 14) $$4.8 \times 10^{3} = 4,800$$ and $$9.6 \times 10^{7} = 96,000,000$$; lesser is $$4.8 \times 10^{3}$$ - 15) $$3.1 \times 10^{-5} = 0.000031$$ and $$7.5 \times 10^{-5} = 0.000075$$; lesser is $$3.1 \times 10^{-5}$$ - 16) $$6.9 \times 10^{-3} = 0.0069$$ and $$4.3 \times 10^{-3} = 0.0043$$; lesser is $$4.3 \times 10^{-3}$$ 7. **Write populations in scientific notation:** - Brazil: 2,080,000 = $$2.08 \times 10^{6}$$ - Fiji: 89,900 = $$8.99 \times 10^{4}$$ - Monaco: 3,800 = $$3.8 \times 10^{3}$$ - Singapore: 56,000 = $$5.6 \times 10^{4}$$ **Final answers:** - 1) No, $$a=71$$ not between 1 and 10 - 2) Yes - 3) No, $$a=0.99$$ less than 1 - 4) Yes - 5) $$5.33 \times 10^{5}$$ - 6) $$3.278 \times 10^{2}$$ - 7) $$3.4 \times 10^{-3}$$ - 8) $$7.28 \times 10^{-6}$$ - 9) 7360 - 10) 24310 - 11) 0.0527 - 12) 0.000401 - 13) $$5.9 \times 10^{3}$$ - 14) $$4.8 \times 10^{3}$$ - 15) $$3.1 \times 10^{-5}$$ - 16) $$4.3 \times 10^{-3}$$ - 17) Brazil: $$2.08 \times 10^{6}$$, Fiji: $$8.99 \times 10^{4}$$, Monaco: $$3.8 \times 10^{3}$$, Singapore: $$5.6 \times 10^{4}$$