Date \( \qquad \) Class \( \qquad \) LESSON Scientific Notation with Negative Powers of 10 Practice and Problem Solving: A/B Write each number as a negative power of ten. 1. \( \frac{1}{10^{2}}= \) \( \qquad \) 2. \( \frac{1}{10^{4}}= \) \( \qquad \) 3. \( \frac{1}{10^{5}}= \) \( \qquad \) 4. \( \frac{1}{10^{7}}= \) \( \qquad \) 5. \( \frac{1}{10^{6}}= \) \( \qquad \) 6. \( \frac{1}{10^{3}}= \) \( \qquad \) 7. \( \frac{1}{10^{9}}= \) \( \qquad \) 8. \( \frac{1}{10^{1}}= \) \( \qquad \) Write each power of ten in standard notation. 9. \( 10^{-3}= \) \( \qquad \) 10. \( 10^{-5}= \) \( \qquad \) 11. \( 10^{-1}= \) \( \qquad \) 12. \( 10^{-6}= \) \( \qquad \) 13. \( 10^{-2}= \) \( \qquad \) 14. \( 10^{-9}= \) \( \qquad \) 15. \( 10^{-4}= \) \( \qquad \) 16. \( 10^{-7}= \) \( \qquad \) Write each number in scientific notation. 17. 0.025 18. 0.3 19. 0.000473 20. 0.0024 \( \qquad \) \( \qquad \) 21. 0.000014565 22. 0.70010 23. 0.0190500 24. 0.00330000 \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) Write each number in standard notation. 25. \( 6 \times 10^{-3} \) 26. \( 4.5 \times 10^{-2} \) 27. \( 7 \times 10^{-7} \) 28. \( 1.05 \times 10^{-6} \) \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) 29. \( 3.052 \times 10^{-8} \) 30. \( 5 \times 10^{-1} \) 31. \( 9.87 \times 10^{-4} \) 32. \( 5.43 \times 10^{-5} \)
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Think of scientific notation as a superpower for handling really big or really small numbers! This notation was popularized in the early 20th century, and it simplifies calculations and comparisons, especially in fields like physics, chemistry, and engineering. Instead of writing out zeros galore, you can focus on the significant figures—the "meat" of your number—by using powers of ten. It's like shorthand for numerically challenging concepts! In the real world, scientific notation is a game changer! When measuring astronomical distances or microscopic particles, regular numbers just won't cut it. For instance, light-years might be expressed as \( 10^{16} \) meters, while a bacterium might be \( 10^{-6} \) meters in size. This shorthand helps scientists and researchers communicate and calculate efficiently without drowning in zeros, making complex calculations a breeze!
