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Learn to express numbers using exponents and scientific notation for problem-solving. Practice writing numbers in standard form and scientific notation with real-world examples.

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  1. Lesson Menu Main Idea and New Vocabulary NGSSS Example 1: Express Numbers in Standard Form Example 2: Express Numbers in Standard Form Example 3: Write Numbers in Scientific Notation Example 4: Write Numbers in Scientific Notation Example 5: Real-World Example Five-Minute Check

  2. Use scientific notation to write large and small numbers. • scientific notation Main Idea/Vocabulary

  3. MA.8.A.6.1 Use exponents and scientific notation to write large and small numbers and vice versa and to solve problems. NGSSS

  4. Express Numbers in Standard Form Write 9.62 × 105 in standard form. 9.62 × 105 = 962,000. The decimal point moves 5 places right. Answer: 962,000 Example 1

  5. Write 7.1 × 103 in standard form. A. 0.0071 B. 0.071 C. 710 D. 7,100 Example 1 CYP

  6. Express Numbers in Standard Form Write 2.85 × 10–6 in standard form. 2.85 × 10–6= 0.00000285 The decimal point moves 6 places left. Answer: 0.00000285 Example 2

  7. Write 5.09 × 10–4 in standard form. A. 0.000509 B. 0.00509 C. 5,090 D. 50,900 Example 2 CYP

  8. Write Numbers in Scientific Notation Write 931,500,000 in scientific notation. 931,500,000= 9.315 × 100,000,000 The decimal point moves 8 places. = 9.315 × 108Since 931,500,000 > 1, the exponent is positive. Answer: 9.315 × 108 Example 3

  9. Write 120,000 in scientific notation. A. 1.2 × 10–5 B. 1.2 × 104 C. 12.0 × 104 D. 1.2 × 105 Example 3 CYP

  10. Write Numbers in Scientific Notation Write 0.00443 in scientific notation. 0.00443 = 4.43 × 0.001The decimal point moves 3 places. = 4.43 × 10–3Since 0 < 0.00443 < 1, the exponent is negative. Answer: 4.443 × 10–3 Example 4

  11. Write 0.000092 in scientific notation. A. 9.2 × 10–6 B. 9.2 × 10–5 C. 92.0 × 10–4 D. 9.2 × 105 Example 4 CYP

  12. VISIBLE LIGHT The following table lists the maximum frequency for the colors of the visible light spectrum. List the colors from greatest to least frequency. Example 5

  13. Since all the maximum frequencies have the same power of ten, compare the factors that are less than 10. 7.5 > 6.7 > 6.1 > 5.1 > 3.8 violet blue green orange red Answer: The colors from greatest to least frequency are violet, blue, green, orange, and red. Example 5

  14. Planet Mass (kg) Earth 5.98  1024 Mars 6.42  1023 Mercury 3.30  1023 Saturn 5.69  1026 Venus 4.87  1024 PLANETS The following table lists the masses of five planets. List the planets from least to greatest mass. A.Mercury, Venus, Saturn, Earth, Mars B.Mars, Mercury, Earth, Venus, Saturn C.Mercury, Mars, Venus, Earth, Saturn D.Mercury, Mars, Saturn, Venus, Earth Example 5 CYP

  15. Write 5.92 × 104 in standard form. A.0.000592 B.592 C. 5,920 D. 59,200 Five Minute Check 1

  16. Write 1.9 × 10–6 in standard form. A.0.0000019 B.0.000019 C.1,900,000 D. 19,000,000 Five Minute Check 2

  17. Write 6.7 × 108 in standard form. A. 67,000,000 B. 670,000,000 C. 6,700,000,000 D. 67,000,000,000 Five Minute Check 3

  18. Write 26,400,000 in scientific notation. A.2.64 × 10–7 B.26.4 × 107 C.2.64 × 107 D.2.64 × 108 Five Minute Check 4

  19. Write 11,000 in scientific notation. A.1.1 × 103 B.1.1 × 104 C.1.1 × 10–4 D.11.0 × 104 Five Minute Check 5

  20. Write 0.000098 in scientific notation. A.9.8 × 10–5 B.9.8 × 10–4 C.0.98 × 10–4 D.9.8 × 105 Five Minute Check 6

  21. The diameter of Jupiter at its equator is approximately 143,000 kilometers. Which of the following correctly shows the diameter in scientific notation? A.1.43 × 10–5 B.1.43 × 10–3 C.1.43 × 103 D.1.43 × 105 Five Minute Check 5

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