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