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Basic Math and Pre-Algebra - Powers of Ten and Scientific Notation

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    Study Guide Basic Math and Pre - Algebra – Powers of Ten and Scien Ɵfi c Nota Ɵ on 1. Quiz: Scien Ɵfi c Nota Ɵ on 1. Question Rewrite in scientific notation. 23.5 × 10 ⁴ Answer Choices • It is already in scientific notation. • 2.35 × 10³ • 2.35 × 10 ⁵ Correct Answer ࿨ ࿩ ࿪ 2.35 × 10 ⁵ Why This Is Correct In scientific notation, the number in front must be between 1 and 10. 23.5 is greater than 10, so move the decimal one place left: 23.5 → 2.35 Since we moved it one place left, increase the exponent by 1: 10 ⁴ → 10 ⁵ So the correct form is 2.35 × 10 ⁵ . 2. Question Rewrite in scientific notation. 0.056 × 10 ⁻ ³

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    Study Guide Answer Choices • It is already in scientific notation. • 5.6 × 10 ⁻ ⁵ • 5.6 × 10 ⁻ ¹ Correct Answer ࿨ ࿩ ࿪ 5.6 × 10 ⁻ ⁵ Why This Is Correct 0.056 is not between 1 and 10. Move the decimal two places right: 0.056 → 5.6 Since we moved right two places, subtract 2 from the exponent: 10 ⁻ ³ → 10 ⁻ ⁵ Final answer: 5.6 × 10 ⁻ ⁵ 3. Question 1.5 × 10 ⁵ = Answer Choices • 0.000015 • 150,000 • 1,500,000 Correct Answer ࿨ ࿩ ࿪ 150,000 Why This Is Correct 10 ⁵ means move the decimal 5 places to the right: 1.5 → 150,000

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    Study Guide 4. Question 27,000 written in scientific notation is Answer Choices • 27 × 10³ • 2.7 × 10 ⁴ • 2.7 × 10 ⁻ ⁴ Correct Answer ࿨ ࿩ ࿪ 2.7 × 10 ⁴ Why This Is Correct Move decimal 4 places left: 27,000 → 2.7 So exponent is 4. 5. Question 7.63 × 10 ⁻ ⁴ = Answer Choices • 0.0000763 • 0.000763 • 76,300 Correct Answer ࿨ ࿩ ࿪ 0.000763 Why This Is Correct 10 ⁻ ⁴ means move decimal 4 places left: 7.63 → 0.000763

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    Study Guide 6. Question 0.000345 written in scientific notation is Answer Choices • 3.45 × 10 ⁻ ⁴ • 3.45 • 3.45 × 10 ⁴ Correct Answer ࿨ ࿩ ࿪ 3.45 × 10 ⁻ ⁴ Why This Is Correct Move decimal 4 places right to make 3.45. So exponent is − 4. 7. Question Which of these values is the greatest? Answer Choices • 5.6 × 10 ⁻ ² • 0.0056 • 0.56 Correct Answer ࿨ ࿩ ࿪ 0.56 Why This Is Correct 5.6 × 10 ⁻ ² = 0.056 0.0056 is smaller 0.56 is the largest.

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    Study Guide 8. Question Which of these values is the least? Answer Choices • 23.4 × 10 ⁻ ³ • 23 × 10 ⁻ ² • 0.235 × 10¹ Correct Answer ࿨ ࿩ ࿪ 23.4 × 10 ⁻ ³ Why This Is Correct 23.4 × 10 ⁻ ³ = 0.0234 23 × 10 ⁻ ² = 0.23 0.235 × 10¹ = 2.35 Smallest is 0.0234. 9. Question Multiply and express in scientific notation. (4 × 10³)(2 × 10 ⁴ ) Answer Choices • 6 × 10 ⁷ • 8 × 10 ⁷ • 8 × 10¹²

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    Study Guide Correct Answer ࿨ ࿩ ࿪ 8 × 10 ⁷ Why This Is Correct Multiply numbers: 4 × 2 = 8 Add exponents: 3 + 4 = 7 10. Question Multiply and express the answer in scientific notation. (5 × 10 ⁵ )(3 × 10³) Answer Choices • 1.5 × 10 ⁷ • 15 × 10 ⁸ • 1.5 × 10 ⁹ Correct Answer ࿨ ࿩ ࿪ 1.5 × 10 ⁹ Why This Is Correct 5 × 3 = 15 Add exponents: 5 + 3 = 8 15 × 10 ⁸ = 1.5 × 10 ⁹ (adjust form) 11. Question Multiply and express the answer in scientific notation. (2.1 × 10 ⁶ )(6 × 10 ⁻ ³) Answer Choices • 1.26 × 10 ⁴ • 1.26 × 10² • 12.6 × 10³

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    Study Guide Correct Answer ࿨ ࿩ ࿪ 1.26 × 10 ⁴ Why This Is Correct 2.1 × 6 = 12.6 6 + ( − 3) = 3 12.6 × 10³ = 1.26 × 10 ⁴ 12. Question Multiply and express the answer in scientific notation. (5 × 10²)(6 × 10³)(7 × 10 ⁴ ) Answer Choices • 2.1 × 10² ⁶ • 2.1 × 10²² • 2.1 × 10¹¹ Correct Answer ࿨ ࿩ ࿪ 2.1 × 10¹¹ Why This Is Correct 5 × 6 × 7 = 210 2 + 3 + 4 = 9 210 × 10 ⁹ = 2.1 × 10¹¹ 13. Question Divide and express the answer in scientific notation. (6 × 10¹²) ÷ (3 × 10 ⁴ )

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    Study Guide Answer Choices • 2 × 10³ • 2 × 10 ⁸ • 3 × 10 ⁸ Correct Answer ࿨ ࿩ ࿪ 2 × 10 ⁸ Why This Is Correct 6 ÷ 3 = 2 12 − 4 = 8 14. Question Divide and express the answer in scientific notation. (4 × 10 ⁻ ⁶ ) ÷ (5 × 10 ⁻ ³) Answer Choices • 0.8 × 10² • 8 × 10 ⁻ ⁴ • 8 × 10 ⁻ ² Correct Answer ࿨ ࿩ ࿪ 8 × 10 ⁻ ⁴ Why This Is Correct 4 ÷ 5 = 0.8 − 6 − ( − 3) = − 3 0.8 × 10 ⁻ ³ = 8 × 10 ⁻ ⁴

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    Study Guide 15. Question Divide and express the answer in scientific notation. (1.2 × 10 ⁶ ) ÷ (4.8 × 10²) Answer Choices • 2.5 × 10³ • 25 × 10³ • 0.25 × 10 ⁴ Correct Answer ࿨ ࿩ ࿪ 2.5 × 10³ Why This Is Correct 1.2 ÷ 4.8 = 0.25 6 − 2 = 4 0.25 × 10 ⁴ = 2.5 × 10³ 16. Question (20 × 10³) ÷ (5 × 10 ⁻ ¹) Answer Choices • 4 × 10 ⁻ ³ • 4 × 10² • 4 × 10 ⁴ Correct Answer ࿨ ࿩ ࿪ 4 × 10 ⁴ Why This Is Correct 20 ÷ 5 = 4 3 − ( − 1) = 4

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    Study Guide 17. Question (12 × 10 ⁻ ⁴ ) ÷ (16 × 10 ⁻ ²) Answer Choices • 7.5 × 10 ⁻ ³ • 7.5 × 10 ⁻ ¹ • 7.5 × 10¹ Correct Answer ࿨ ࿩ ࿪ 7.5 × 10 ⁻ ³ Why This Is Correct 12 ÷ 16 = 0.75 − 4 − ( − 2) = − 2 0.75 × 10 ⁻ ² = 7.5 × 10 ⁻ ³ 18. Question Which row has all equal values? Answer Choices • 0.25 × 10 ⁶ ; 2.5 × 10 ⁷ ; 25 × 10 ⁸ • 0.028 × 10 ⁻ ¹; 2.8 × 10 ⁻ ²; 280 × 10 ⁻ ³ • 0.5 × 10³; 50 × 10¹; 500 × 10 ⁰ Correct Answer ࿨ ࿩ ࿪ 0.028 × 10 ⁻ ¹; 2.8 × 10 ⁻ ²; 280 × 10 ⁻ ³ Why This Is Correct All equal 0.0028.

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