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

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Study GuideBasic Math and Pre-Algebra–Powers of Ten andScienƟfic NotaƟon1. Quiz: ScienƟfic NotaƟon1. QuestionRewrite in scientific notation.23.5 × 10⁴Answer Choices•It is already in scientific notation.•2.35 × 10³•2.35 × 10⁵Correct Answer࿨࿩࿪2.35 × 10⁵Why This Is CorrectIn 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→2.35Since we moved it one place left, increase the exponent by 1:10⁴→10⁵So the correct form is2.35 × 10⁵.2. QuestionRewrite in scientific notation.0.056 × 10⁻³

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Study GuideAnswer Choices•It is already in scientific notation.•5.6 × 10⁻⁵•5.6 × 10⁻¹Correct Answer࿨࿩࿪5.6 × 10⁻⁵Why This Is Correct0.056 is not between 1 and 10.Move the decimal two places right:0.056→5.6Since we moved right two places, subtract 2 from the exponent:10⁻³→10⁻⁵Final answer:5.6 × 10⁻⁵3. Question1.5 × 10⁵=Answer Choices•0.000015•150,000•1,500,000Correct Answer࿨࿩࿪150,000Why This Is Correct10⁵means move the decimal 5 places to the right:1.5→150,000

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Study Guide4. Question27,000 written in scientific notation isAnswer Choices•27 × 10³•2.7 × 10⁴•2.7 × 10⁻⁴Correct Answer࿨࿩࿪2.7 × 10⁴Why This Is CorrectMove decimal 4 places left:27,000→2.7So exponent is 4.5. Question7.63 × 10⁻⁴=Answer Choices•0.0000763•0.000763•76,300Correct Answer࿨࿩࿪0.000763Why This Is Correct10⁻⁴means move decimal 4 places left:7.63→0.000763

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Study Guide6. Question0.000345 written in scientific notation isAnswer Choices•3.45 × 10⁻⁴•3.45•3.45 × 10⁴Correct Answer࿨࿩࿪3.45 × 10⁻⁴Why This Is CorrectMove decimal 4 places right to make 3.45.So exponent is−4.7. QuestionWhich of these values is the greatest?Answer Choices•5.6 × 10⁻²•0.0056•0.56Correct Answer࿨࿩࿪0.56Why This Is Correct5.6 × 10⁻² = 0.0560.0056 is smaller0.56 is the largest.

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Study Guide8. QuestionWhich of these values is the least?Answer Choices•23.4 × 10⁻³•23 × 10⁻²•0.235 × 10¹Correct Answer࿨࿩࿪23.4 × 10⁻³Why This Is Correct23.4 × 10⁻³ = 0.023423 × 10⁻² = 0.230.235 × 10¹ = 2.35Smallest is 0.0234.9. QuestionMultiply and express in scientific notation.(4 × 10³)(2 × 10⁴)Answer Choices•6 × 10⁷•8 × 10⁷•8 × 10¹²

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Study GuideCorrect Answer࿨࿩࿪8 × 10⁷Why This Is CorrectMultiply numbers: 4 × 2 = 8Add exponents: 3 + 4 = 710. QuestionMultiply and express the answer in scientific notation.(5 × 10⁵)(3 × 10³)Answer Choices•1.5 × 10⁷•15 × 10⁸•1.5 × 10⁹Correct Answer࿨࿩࿪1.5 × 10⁹Why This Is Correct5 × 3 = 15Add exponents: 5 + 3 = 815 × 10⁸= 1.5 × 10⁹(adjust form)11. QuestionMultiply and express the answer in scientific notation.(2.1 × 10⁶)(6 × 10⁻³)Answer Choices•1.26 × 10⁴•1.26 × 10²•12.6 × 10³

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Study GuideCorrect Answer࿨࿩࿪1.26 × 10⁴Why This Is Correct2.1 × 6 = 12.66 + (−3) = 312.6 × 10³ = 1.26 × 10⁴12. QuestionMultiply and express the answer in scientific notation.(5 × 10²)(6 × 10³)(7 × 10⁴)Answer Choices•2.1 × 10²⁶•2.1 × 10²²•2.1 × 10¹¹Correct Answer࿨࿩࿪2.1 × 10¹¹Why This Is Correct5 × 6 × 7 = 2102 + 3 + 4 = 9210 × 10⁹= 2.1 × 10¹¹13. QuestionDivide and express the answer in scientific notation.(6 × 10¹²) ÷ (3 × 10⁴)

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Study GuideAnswer Choices•2 × 10³•2 × 10⁸•3 × 10⁸Correct Answer࿨࿩࿪2 × 10⁸Why This Is Correct6 ÷ 3 = 212−4 = 814. QuestionDivide and express the answer in scientific notation.(4 × 10⁻⁶) ÷ (5 × 10⁻³)Answer Choices•0.8 × 10²•8 × 10⁻⁴•8 × 10⁻²Correct Answer࿨࿩࿪8 × 10⁻⁴Why This Is Correct4 ÷ 5 = 0.8−6−(−3) =−30.8 × 10⁻³ = 8 × 10⁻⁴

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Study Guide15. QuestionDivide and express the answer in scientific notation.(1.2 × 10⁶) ÷ (4.8 × 10²)Answer Choices•2.5 × 10³•25 × 10³•0.25 × 10⁴Correct Answer࿨࿩࿪2.5 × 10³Why This Is Correct1.2 ÷ 4.8 = 0.256−2 = 40.25 × 10⁴= 2.5 × 10³16. Question(20 × 10³) ÷ (5 × 10⁻¹)Answer Choices•4 × 10⁻³•4 × 10²•4 × 10⁴Correct Answer࿨࿩࿪4 × 10⁴Why This Is Correct20 ÷ 5 = 43−(−1) = 4

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Study Guide17. Question(12 × 10⁻⁴) ÷ (16 × 10⁻²)Answer Choices•7.5 × 10⁻³•7.5 × 10⁻¹•7.5 × 10¹Correct Answer࿨࿩࿪7.5 × 10⁻³Why This Is Correct12 ÷ 16 = 0.75−4−(−2) =−20.75 × 10⁻² = 7.5 × 10⁻³18. QuestionWhich row has all equal values?Answer Choices•0.25 × 10⁶; 2.5 × 10⁷; 25 × 10⁸•0.028 × 10⁻¹; 2.8 × 10⁻²; 280 × 10⁻³•0.5 × 10³; 50 × 10¹; 500 × 10⁰Correct Answer࿨࿩࿪0.028 × 10⁻¹; 2.8 × 10⁻²; 280 × 10⁻³Why This Is CorrectAll equal 0.0028.

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