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Express Numbers in Standard and Scientific Form

Learn how to express numbers in standard form and scientific notation. Practice writing numbers in both forms and understand the rules for moving the decimal point. Apply these concepts to real-world examples.

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Express Numbers in Standard and Scientific Form

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  1. Lesson Menu Main Idea and New Vocabulary 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

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

  3. 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

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

  5. 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

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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

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