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Worksheet

Comparing Numbers in Scientific Notation

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Show your work for each problem.

  1. 1.
    Which number is greater: 8.9×1068.9 \times 10^6 or 5.2×1075.2 \times 10^7?
    1. a)5.2×1075.2 \times 10^7
    2. b)They are equal
    3. c)You cannot tell without writing out the zeros
    4. d)8.9×1068.9 \times 10^6
  2. 2.
    How many times as large as 10410^4 is 10710^7?
  3. 3.
    Compare 7.1×1097.1 \times 10^9 and 2.3×10112.3 \times 10^{11}.
  4. 4.
    Which symbol makes this true? 3.4×105  □  3.9×1053.4 \times 10^5 \;\square\; 3.9 \times 10^5
    1. a)>>
    2. b)==
    3. c)<<
    4. d)None of them, they cannot be compared
  5. 5.
    Normalize before comparing: 45×103=4.5×10n45 \times 10^3 = 4.5 \times 10^n. What is nn?
  6. 6.
    Compare 6.25×1046.25 \times 10^4 and 6.3×1046.3 \times 10^4.
  7. 7.
    Which number is the smallest?
    1. a)4×10−54 \times 10^{-5}
    2. b)4×10−44 \times 10^{-4}
    3. c)4×10−34 \times 10^{-3}
    4. d)4×10−24 \times 10^{-2}
  8. 8.
    Which is greater, 6×10−46 \times 10^{-4} or 6×10−26 \times 10^{-2}? Type the exponent of the greater number.
  9. 9.
    Compare 38×10538 \times 10^5 and 4.1×1064.1 \times 10^6.
  10. 10.
    Which number is equal to 56×10356 \times 10^3?
    1. a)5.6×1025.6 \times 10^2
    2. b)5.6×1045.6 \times 10^4
    3. c)0.56×1040.56 \times 10^4
    4. d)5.6×1055.6 \times 10^5
  11. 11.
    How many times as large as 5×1055 \times 10^5 is 5×1095 \times 10^9?
  12. 12.
    Compare 5×10−45 \times 10^{-4} and 8×10−68 \times 10^{-6}.
  13. 13.
    Compare 0.7×10−30.7 \times 10^{-3} and 6.5×10−56.5 \times 10^{-5}.
  14. 14.
    Which list is ordered from smallest to largest?
    1. a)2.5×10−3, 31×10−4, 9×10−4, 1.2×10−22.5 \times 10^{-3},\ 31 \times 10^{-4},\ 9 \times 10^{-4},\ 1.2 \times 10^{-2}
    2. b)9×10−4, 2.5×10−3, 31×10−4, 1.2×10−29 \times 10^{-4},\ 2.5 \times 10^{-3},\ 31 \times 10^{-4},\ 1.2 \times 10^{-2}
    3. c)1.2×10−2, 2.5×10−3, 9×10−4, 31×10−41.2 \times 10^{-2},\ 2.5 \times 10^{-3},\ 9 \times 10^{-4},\ 31 \times 10^{-4}
    4. d)9×10−4, 31×10−4, 2.5×10−3, 1.2×10−29 \times 10^{-4},\ 31 \times 10^{-4},\ 2.5 \times 10^{-3},\ 1.2 \times 10^{-2}
  15. 15.
    How many times as large as 2×10−82 \times 10^{-8} is 2×10−32 \times 10^{-3}?
  16. 16.
    Order from smallest to largest: 3.2×1053.2 \times 10^5, 9.1×1049.1 \times 10^4, 30×10430 \times 10^4, 1.05×1061.05 \times 10^6.
  17. 17.
    Light travels about 3×1083 \times 10^8 m/s. Sound in air travels about 3×1023 \times 10^2 m/s. About how many times as fast is light?
  18. 18.
    A human hair is about 8×10−58 \times 10^{-5} m wide. A virus is about 1×10−71 \times 10^{-7} m across. How many times as wide as the virus is the hair?
Interactive lesson with step-by-step solutions and more practice (free): mathorio.com/en/learn/arithmetic/scientific-notation/comparing-scientific-notation
Today's challengeOne problem, three tries