Intermediate Algebra Problems With Answers -
Sample 5 - Scientific Notation

A set of intermediate algebra problems, related to scientific notation, with answers, are presented. The solutions are at the bottom of the page.


Review: A number x is written in scientific notation when it is written in the form:
x = a × 10 N

with 1 ≤ |a| < 10 and N is an integer.

  1. Convert from decimal notation to scientific notation.
    a) 234
    b) 0.000052
    c) -220,000
    d) -0.00000000000000182

  2. Convert from scientific to decimal notation.
    a) 1.01 × 10 2
    b) 8.2 × 10 -6
    c) 3.456 × 10 10
    d) -1.2 × 10 -8

  3. Perform the multiplication and write the result in scientific notation.
    a) (5 × 10 2)(7 × 10 5)
    b) (1.2 × 10 -6)(3.5 × 10 14)
    c) (-4.5 × 10 -7)(8.62 × 10 10)
    d) (-7.2 × 10 -6)(0.00039)

  4. Perform the division and write the result in scientific notation.
    a) (4 × 10 13) / (5 × 10 -4)
    b) 0.000012 / (2.4 × 10 -8)
    c) (-1.2 × 10 -6) / (1.5 × 10 -10)
    d) 0.00000065 / 0.000013

  5. Evaluate and express in scientific notation.
    a) (1.3 × 10 -6) 2
    b) (1.5 × 10 -8) 2(2.1 × 10 5)
    c) [ (1.144 × 10 2)(6 × 10 7) ] / (2.2 × 10 4)
    d) [ (0.00001)(2,500) ] / [ (0.0003)(150,000) ]

  6. Evaluate in scientific notation.
    a) The diameter of an atom: 0.0000000000001 meter
    b) diameter of earth = 12,756,000 meters
    c) 1 billion: 1000,0000,000
    d) 1 micron: 0.000001 meter
    e) 1 trillion: 1000,000,000,000
    f) Diameter of earth / diameter of atom
    g) Speed of light: 300,000,000 m/sec
    h) Distance travelled by light in one year.

Answers to the Above Questions

  1. a) 234 = 2.34× 10 2
    b) 0.000052 = 5.2× 10 -5
    c) -220,000 = -2.2× 10 5
    d) -0.00000000000000182 = -1.82× 10 -15

  2. a) 1.01 × 10 2 = 101
    b) 8.2 × 10 -6 = 0.0000082
    c) 3.456 × 10 10 = 34560000000
    d) -1.2 × 10 -8 = -0.000000012


  3. a) (5 × 10 2)(7 × 10 5)
    = (5 × 7)(10 2 × 10 5)
    = 35 × 10 7 = 3.5 × 10 8

    b) (1.2 × 10 -6)(3.5 × 10 14)
    = (1.2×3.5)(10 -6 × 10 14)
    = 4.2 × 10 8

    c) (- 4.5 × 10 -7)(8.62 × 10 10)
    = (- 4.5 × 8.62)(10 -7 × 10 10)
    = - 38.79 × 10 3 = - 3.879 × 10 4

    d) (- 7.2 × 10 -6)(0.00039)
    = (- 7.2 × 10 -6)(3.9 × 10 -4)
    = (- 7.2 × 3.9)(10 -6 × 10 -4)
    = - 28.08 × 10 -10 = - 2.808 × 10 -9

  4. a) (4 × 10 13) / (5 × 10 -4) = (4/5)(10 13 / 10 -4) = 0.8 × 10 17 = 8.0 × 10 16

    b) 0.000012 / (2.4 × 10 -8) = (0.000012 / 2.4)(1 / 10 -8) = (0.000005)(1 / 10 -8)
    = (5.0 × 10 -6)(10 8) = 5.0 × 10 2

    c) (-1.2 × 10 -6) / (1.5 × 10 -10) = (-1.2 / 1.5)(10 -6 / 10 -10)
    = -0.8 × 10 4 = -8.0 × 10 3

    d) 0.00000065 / 0.000013 = 0.05 = 5.0 × 10 -2

  5. a) (1.3 × 10 -6) 2 = (1.3) 2 (10 -6) 2 = 1.69 × 10 -12

    b) (1.5 × 10 -8) 2(2.1 × 10 5) = 1.5 2 (10 -8) 2 (2.1 × 10 5)
    = (2.25 × 10 -16)(2.1 × 10 5) = 4.725 × 10 -11

    c) [ (1.144 × 10 2)(6 × 10 7) ] / (2.2 × 10 4) = (6.864 × 10 9) / (2.2 × 10 4)
    = (6.864 / 2.2) (10 9 / 10 4) = 3.12 × 10 5

    d) [ (0.00001)(2,500) ] / [ (0.0003)(150,000) ] = 0.025 / 45 = 0.000555 = 5.6 × 10 -4


  6. a) The diameter of an atom: 0.0000000001 meter = 1.0 × 10 -9 meter
    b) diameter of earth = 12,756,000 meters = 1.2756 × 10 7 meters
    c) 1 billion: 1000,0000,000 = 1.0 × 10 9
    d) 1 micron: 0.000001 meter = 1.0 × 10 -6
    e) 1 trillion: 1000,000,000,000 = 1.0 × 10 12
    f) Diameter of earth / diameter of atom = 1.2756 × 10 7 / 1.0 × 10 -9 = 1.2756 × 10 16
    g) Speed of light: 300,000,000 meters per second = 3.0 10 8 m/s
    h) Distance travelled by light in one year:
    There are (365 * 24 * 60 * 60) = 3.1536 × 10 7 seconds in one year.
    Distance travelled by light in one year = time * speed of light
    = (3.1536 × 10 7)(3.0 10 8) = 9.4608 × 10 15 meters = 9.4608 × 10 12 kilometers

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