Solved Examples and Worksheet for Operations with Scientific Notations

Q1Solve the expression (7.5 × 108) (6.6 × 104) and express the result in scientific notation.

A. 4.95
B. 4.95 x 1011
C. 4.95 x 1012
D. 4.95 x 1013

Solutions
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Step: 1
(7.5 x 108) (6.6 x 104) = (7.5 x 6.6) (108 x 104)
  [Use multiplication properties.]
Step: 2
= 49.5 x 1012
  [Use product of powers property.]
Step: 3
= (4.95 x 101) x 1012
  [Write 49.5 in scientific notation.]
Step: 4
= 4.95 x 1013
  [Use product of powers property.]
Correct Answer is :   4.95 x 1013
Q2Solve (5.6 × 107) (7.3 × 10-2) and write the result in scientific notation.
A. 4.088 x 106
B. 4.088
C. 4.088 x 105
D. 4.088 x 10-6

Solutions
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Step: 1
(5.6 x 107) (7.3 x 10-2) = (5.6 x 7.3) (107 x 10-2)
  [Use multiplication properties.]
Step: 2
= (40.88) (105)
  [Use product of powers property.]
Step: 3
= (4.088 x 101) x 105
  [Write 40.88 in scientific notation.]
Step: 4
= 4.088 x 106
  [Use product of powers property.]
Correct Answer is :   4.088 x 106
Q3Simplify (0.64 × 105) / (3.2 × 10-2) and write the result in scientific notation.
A. 2.0 x 106
B. -2.0 x 106
C. 2.0 x 107
D. 2.0 x 10-6

Solutions
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Step: 1
(0.64 x 105) / (3.2 x 10-2) = (0.643.2) x (105 / 10-2)
  [Write as a product.]
Step: 2
= 0.2 x (107)
  [Use quotient of powers property.]
Step: 3
= (2.0 x 10-1) x 107
  [Write 0.2 in scientific notation.]
Step: 4
= 2.0 x 106
  [Use product of powers property.]
Correct Answer is :   2.0 x 106
Q4Simplify (4.0 × 10-4) / (12 × 10-2) and write the result in scientific notation.

A. 3.3 x 10-3
B. 3.3 x 103
C. -3.3 x 10-3
D. -3.3 x 103

Solutions
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Step: 1
(4.0 x 10-4) / (12 x 10-2) = (4.012) x (10-4 / 10-2)
  [Write as a product.]
Step: 2
= 0.33 x 10-2
  [Use quotient of powers property.]
Step: 3
= (3.3 x 10-1) x 10-2
  [Write 0.33 in scientific notation.]
Step: 4
= 3.3 x 10-3
  [Use product of powers property.]
Correct Answer is :   3.3 x 10-3
Q5Solve the expression (7.4 × 106)(3.2 × 102) and express the result in scientific notation.
A. 2.368 × 107
B. 2.368 × 108
C. 2.368
D. 2.368 × 109

Solutions
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Step: 1
(7.4 × 106)(3.2 × 102) = (7.4 × 3.2)(106 × 102)
  [Use multiplication properties.]
Step: 2
= 23.68 × 108
  [Use product of powers property.]
Step: 3
= (2.368 × 101) × 108
  [Write 23.68 in scientific notation.]
Step: 4
= 2.368 × 109
  [Use product of powers property.]
Correct Answer is :   2.368 × 109
Q6Simplify :0.96×1032.4×10- 4 and write the result in scientific notation.
A. 0.4 × 106
B. 4.0 × 104
C. 4.0 × 107
D. 4.0 × 106

Solutions
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Step: 1
0.96×1032.4×10- 4 = (0.962.4) × 10310- 4
  [Write as a product.]
Step: 2
= 0.4 × (107)
  [Use quotient of powers property.]
Step: 3
= (4.0 × 10- 1) × 107
  [Write 0.4 in scientific notation.]
Step: 4
= 4.0 × 106
  [Use product of powers property.]
Correct Answer is :   4.0 × 106
Q7Simplify 2.0×10- 1110×10- 8 and write the result in scientific notation.

A. 2 × 104
B. - 2 × 10- 4
C. 2 × 10- 4
D. - 2 × 104

Solutions
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Step: 1
2.0×10- 1110×10- 8 = (2.010) × 10- 1110- 8
  [Write as a product.]
Step: 2
= 0.2 × 10- 3
  [Use quotient of powers property.]
Step: 3
= (2 × 10- 1) × 10- 3
  [Write 0.2 in scientific notation.]
Step: 4
= 2 × 10- 4
  [Use product of powers property.]
Correct Answer is :   2 × 10- 4
Q8Express the product in scientific notation.
(1.6 × 10 2) (1.2 × 10 -5)
A. 2.9 × 10 - 3
B. 0.9× 10 - 3
C. 1.9 × 10 -3
D. none of the above

Solutions
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Step: 1
Any non zero digit, or any zero which serves a purpose other than to locate the decimal point is a significant digit.
Step: 2
(1.6 × 10 2 ) (1.2 × 10 - 5)
Step: 3
= (1.6 × 1.2)(10 2 × 10 - 5)
  [Rearrange factors.]
Step: 4
= 1.92 × 10 - 3
  [When two exponents having the same base are multiplied, their powers are added.]
Step: 5
The given two numbers have 2 significant digits.
Step: 6
≈ 1.9 × 10 - 3
  [Approximate to 2 significant digits.]
Correct Answer is :    1.9 × 10 -3
Q9Solve the expression (6.8 × 108) (5.7 × 108) and express the result in scientific notation.
A. 3.876 × 1015
B. 3.876 × 1017
C. 3.876 × 1016
D. 3.876

Solutions
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Step: 1
(6.8 × 108) (5.7 × 108) = (6.8 × 5.7) (108 × 108)
  [Use multiplication properties.]
Step: 2
= 38.76 × 1016
  [Use product of powers property.]
Step: 3
= (3.876 × 101) × 1016
  [Write 38.76 in scientific notation.]
Step: 4
= 3.876 × 1017
  [Use product of powers property.]
Correct Answer is :   3.876 × 1017
Q10Solve (5.9 × 106) (4.3 × 10- 3) and write the result in scientific notation.
A. 2.537 × 104
B. 2.537 × 103
C. 2.537 × 10-4
D. 2.537

Solutions
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Step: 1
(5.9 × 106) (4.3 × 10- 3) = (5.9 × 4.3) (106 × 10- 3)
  [Use multiplication properties.]
Step: 2
= (25.37) (103)
  [Use product of powers property.]
Step: 3
= (2.537 × 101) × 103
  [Write 25.37 in scientific notation.]
Step: 4
= 2.537 × 104
  [Use product of powers property.]
Correct Answer is :   2.537 × 104
Q11Simplify 5.0 ×10- 820 ×10- 5 and express the result in scientific notation.
A. 2.5 × 104
B. - 2.5 × 104
C. 2.5 × 10 - 4
D. - 2.5 × 10 - 4

Solutions
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Step: 1
5.0 ×10- 820 ×10- 5 = 5.020  ×10- 810- 5
  [Write as a product.]
Step: 2
= 0.25 × 10 - 3
  [Use quotient of powers property.]
Step: 3
= (2.5 × 10 - 1) × 10 - 3
  [Write 0.25 in scientific notation.]
Step: 4
= 2.5 × 10 - 4
  [Use product of powers property.]
Correct Answer is :   2.5 × 10 - 4
Q12Solve (7.5 × 107) (6.8 × 10- 3) and write the result in scientific notation.

A. 5.100 × 104
B. 5.100 × 105
C. 5.100
D. 5.100 × 10-5

Solutions
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Step: 1
(7.5 × 107) (6.8 × 10- 3) = (7.5 × 6.8) (107 × 10- 3)
  [Use multiplication properties.]
Step: 2
= (51) (104)
  [Use product of powers property.]
Step: 3
= (5.100 × 101) × 104
  [Write 51 in scientific notation.]
Step: 4
= 5.100 × 105
  [Use product of powers property.]
Correct Answer is :   5.100 × 105
Q13Evaluate 2.0 × 10- 106 ×  10- 5 in scientific notation.
A. 3.33 × 10 - 6
B. - 3.33 × 10 - 6
C. - 3.33 × 106
D. 3.33 × 106

Solutions
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Q14Evaluate the expression (5.7 × 10-5)(2 × 106) in scientific notation.
A. 1.81 × 1014
B. 1.71 × 1014
C. 1.14 × 102
D. 1.61 × 1014

Solutions
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Step: 1
(5.7 × 10-5)(2 × 106)
  [Original expression.]
Step: 2
= (5.7 × 2)(10-5 × 106)
  [Use Associative and Commutative properties.]
Step: 3
= 11.4 × 101
  [5.7 × 2 = 11.4, 10-5 × 106 = 10-5 + 6 = 101.]
Step: 4
= 1.14 × 102
Correct Answer is :   1.14 × 102
Q15Evaluate 2.3 × 10- 106 ×  10- 5 in scientific notation.

A. - 3.83 × 10 - 6
B. 3.83 × 10 - 6
C. - 3.83 × 106
D. 3.83 × 106

Solutions
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Step: 1
2.3 ×10- 106 ×10- 5 = 2.36  ×10- 1010- 5
  [Write as a product.]
Step: 2
= 0.383 × 10 - 5
  [Use quotient of powers property.]
Step: 3
= (3.83 × 10 - 1) × 10 - 5
  [Write 0.383 in scientific notation.]
Step: 4
= 3.83 × 10 - 6
  [Use product of powers property.]
Correct Answer is :   3.83 × 10 - 6

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