Scientific Notation: Multiplication, Division, Addition And Subtraction

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Scientific Notation: Multiplication, Division, Addition And Subtraction - Quiz

Performing mathematical computations with scientific notation.


Questions and Answers
  • 1. 

    Is the following numbers in proper scientific notation? 23.2 x 102

    • A.

      Yes, this is proper scientific notation

    • B.

      No, this is not proper scientific notation

    Correct Answer
    B. No, this is not proper scientific notation
    Explanation
    2.32 x 10^3

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  • 2. 

    Do NOT use your calculator. UNDERSTAND how to work with scientific notation!(1012 is the same as 10^12)(3.0x 107) (4.0 x 105)  =

    • A.

      12.0 x 10^12

    • B.

      12.0 x 10^35

    • C.

      1.2 x 10^13

    • D.

      1.2 x 10^36

    Correct Answer
    C. 1.2 x 10^13
    Explanation
    When MULTIPLYING in scientific notation, ADD the exponent.
    Make sure you change your answer to proper scientific notation. (3.0x 10^7) (4.0 x 10^5)= (3.0 x 4.0)x 10^(7+5)

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  • 3. 

    Find the answer:  9.0 x 103                          3.0 x 102

    • A.

      3.0 x 10^5

    • B.

      3.0 x 10^6

    • C.

      3.0 x 10^1

    • D.

      3

    • E.

      3.0 x 10^-1

    Correct Answer
    C. 3.0 x 10^1
    Explanation
    Dividing scientific notation: SUBTRACT the exponenent in the numerator from the exponent in the demoninator:
    9.0 x 10^3 divided by 3.0 x 10^2 =
    (9 divided by 3)x 10^(3-2)

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  • 4. 

    (8.0 x 10-2)  x  (3 x 10-3)  =

    • A.

      2.4 x 10^-5

    • B.

      24.0 x 10^-5

    • C.

      24.0 x 10^-6

    • D.

      2.4 x 10^-4

    Correct Answer
    D. 2.4 x 10^-4
    Explanation
    When multiplying with scientific notation: add the exponents.
    (8.0 x 10^-2) x (3 x 10^-3) = (8 x 3)x 10^(-2 + -3) = 24 x 10^-5 = 2.4 x 10^-4

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  • 5. 

    (3.0 x 102) + (4.0 x 103) =

    • A.

      4.3 x 10^2

    • B.

      7.0 x 10^-1

    • C.

      4.3 x 10^3

    • D.

      7.0 x 10^5

    Correct Answer
    C. 4.3 x 10^3
    Explanation
    Adding and Substracting in Scientific Notation REQUIRES the exponents to be the SAME. EASIEST way to do this problem:
    Change into "regular numbers" and then put your answer in proper scientific format:
    (3.0 x 10^2) + (4.0 x 10^3) = 300 + 4,000 = 4,300 =
    4.3 x 10^3

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  • 6. 

    (9.0 x 103)  -  (4.0 x 102)

    • A.

      5.0 x 10^1

    • B.

      13.0 x 10^5

    • C.

      9.4 x 10^3

    • D.

      5.0 x 10^5

    • E.

      8.6 x 10^3

    Correct Answer(s)
    C. 9.4 x 10^3
    E. 8.6 x 10^3
    Explanation
    When substrating in scientific notation, the exponents MUST be the same. EASIEST way to do the problem: Change to "regular numbers", calculate and then change your answer back to scientific notation: (9.0 x 10^3)-(4.0 x 10^2)=
    9,000 - 400 = 8,600 = 8.6 x 10^3

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  • 7. 

     (6.0 x 102) x (5.0 x 104)  =              (2.0 x 10 3)

    • A.

      1.5 x 10^4

    • B.

      1.5 x 10^8

    • C.

      15 x 10^4

    • D.

      6.0 x 10^4

    Correct Answer
    A. 1.5 x 10^4
    Explanation
    (6 x 5 divided by 2)x 10 ^ (2 + 4 -3)= 15 x 10^3
    = 1.5 x 10^4

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  • 8. 

    (6.0 x 102) + (4.0 x 104) =            (2.0 x 102)

    • A.

      5.0 x 10^4

    • B.

      2.03 x 10^2

    • C.

      1.2 x 10^8

    • D.

      5.0 x 10^5

    Correct Answer
    B. 2.03 x 10^2
    Explanation
    Change the numerator into "regular" numbers, calculate and change back to scientific notation (40,000 + 600 = 40,600 = 4.06 x 10^4) then divide by 2.0 x 10^2)

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  • 9. 

    (8.0 x 10-2)   =  (2 x 10-3)    

    • A.

      2 x 10^1 = 20

    • B.

      4 x 10^1 = 40

    • C.

      4 x 10^-5

    • D.

      4.0 x 10^-1

    Correct Answer
    B. 4 x 10^1 = 40
    Explanation
    Division: Subtract the exponents: (-2) - (-3) = +1

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  • 10. 

    What is this equivalent to? 6.2 x 10-3

    • A.

      .062

    • B.

      .62

    • C.

      0.0062

    • D.

      6,200

    Correct Answer
    C. 0.0062
    Explanation
    The given number, 6.2 x 10-3, is in scientific notation. In scientific notation, the number is expressed as a decimal number multiplied by a power of 10. In this case, 6.2 x 10-3 means 6.2 multiplied by 10 raised to the power of -3. To convert this to a decimal number, we move the decimal point three places to the left, resulting in 0.0062. Therefore, the correct answer is 0.0062.

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  • Current Version
  • Oct 13, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Jul 22, 2010
    Quiz Created by
    Kwchiro
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