 # 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.

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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