Here’s the breakdown for the scientific notation problems and simplifications:

Write each number in scientific notation

7. 3340

• Move the decimal 3 places left: $3.34 \times 10^3$

8. 128

• Move the decimal 2 places left: $1.28 \times 10^2$

9. 3,000,000

• Move the decimal 6 places left: $3.0 \times 10^6$

10. 583,000,000

• Move the decimal 8 places left: $5.83 \times 10^8$

11. 0.0000000405

• Move the decimal 8 places right: $4.05 \times 10^{-8}$

12. 0.398

• Move the decimal 1 place right: $3.98 \times 10^{-1}$

Simplify and write each answer in scientific notation

13. $(6 \times 10^1)(9.4 \times 10^{-2})$

• Multiply coefficients: $6 \times 9.4 = 56.4$
• Combine powers of 10: $10^1 \times 10^{-2} = 10^{-1}$
• Final: $5.64 \times 10^0$ or $5.64$

14. $(7.6 \times 10^6)(9 \times 10^{-1})$

• Multiply coefficients: $7.6 \times 9 = 68.4$
• Combine powers of 10: $10^6 \times 10^{-1} = 10^5$
• Adjust: $68.4 = 6.84 \times 10^1$
• Final: $6.84 \times 10^6$

15. $(9.2 \times 10^{-1})(5 \times 10^6)$

• Multiply coefficients: $9.2 \times 5 = 46$
• Combine powers of 10: $10^{-1} \times 10^6 = 10^5$
• Adjust: $46 = 4.6 \times 10^1$
• Final: $4.6 \times 10^6$

16. $(6 \times 10^1)(9.6 \times 10^1)$

• Multiply coefficients: $6 \times 9.6 = 57.6$
• Combine powers of 10: $10^1 \times 10^1 = 10^2$
• Adjust: $57.6 = 5.76 \times 10^1$
• Final: $5.76 \times 10^3$

17. $(3 \times 10^5)(5.3 \times 10^{-6})$

• Multiply coefficients: $3 \times 5.3 = 15.9$
• Combine powers of 10: $10^5 \times 10^{-6} = 10^{-1}$
• Adjust: $15.9 = 1.59 \times 10^1$
• Final: $1.59 \times 10^0$ or $1.59$

18. $(8 \times 10^0)(5.4 \times 10^{-3})$

• Multiply coefficients: $8 \times 5.4 = 43.2$
• Combine powers of 10: $10^0 \times 10^{-3} = 10^{-3}$
• Adjust: $43.2 = 4.32 \times 10^1$
• Final: $4.32 \times 10^{-2}$

Need more details?

Would you like step-by-step solutions for any specific problem? Let me know!

Related Questions:

1. How do you convert large numbers into scientific notation?
2. What are the rules for multiplying powers of 10?
3. How do you simplify numbers that exceed $10$ after multiplication?
4. How can you convert decimals into scientific notation?
5. What’s the difference between positive and negative exponents in scientific notation?

Tip:

When multiplying numbers in scientific notation, first handle the coefficients (numbers) and then combine the powers of 10 by adding their exponents.