Solved Examples and Worksheet for Comparing and Ordering Numbers in Scientific Notation

Q1Which of the numbers is greater, 7 × 103 or 6 × 104?

A. 7 x 103
B. 6 x 104
C. Both are same
D. None of the above

Solutions
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Step: 1
Since 4 > 3, 104 > 103
  [Order the exponents of two numbers.]
Step: 2
6 x 104 > 7 x 103
  [Compare the two numbers and order from greatest to least.]
Step: 3
The number 6 x 104 is greater.
Correct Answer is :   6 x 104
Q2Arrange the numbers 40, 46, 44, 48 from the least to the greatest.

A. 40, 44, 46, 48
B. 44, 40, 48, 46
C. 40, 46, 48, 44
D. 48, 40, 46, 44

Solutions
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Step: 1
0 < 4 < 6 < 8
  [Order the exponents.]
Step: 2
So, 40 < 44 < 46 < 48.
Step: 3
The order of the numbers from least to highest is 40, 44, 46, 48.
Correct Answer is :   40, 44, 46, 48
Q3Order the numbers 389 × 102, 32.3 × 105, 0.079 × 104 from the greatest to the least.
A. 32.3 x 105 > 389 x 102 > 0.079 x 104
B. 389 x 102 > 32.3 x 105 > 0.079 x 104
C. 0.079 x 104 > 32.3 x 105 > 389 x 102
D. None of the above

Solutions
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Step: 1
389 x 102 = 3.89 x 102 x 102
  [Write 389 as 3.89 x 102.]
Step: 2
= 3.89 x 104
  [Add the exponents.]
Step: 3
= 38900
  [Simplify.]
Step: 4
32.3 x 105 = 3.23 x 101 x 105
  [Write 32.3 as 3.23 x 101.]
Step: 5
= 3.23 x 106
  [Add the exponents.]
Step: 6
= 3230000
  [Simplify.]
Step: 7
0.079 x 104 = 7.900 x 10-2 x 104
  [Write 0.079 as 7.900 x 10-2.]
Step: 8
= 7.900 x 102
  [Add the exponents.]
Step: 9
= 790
  [Simplify.]
Step: 10
Since 3230000 > 38900 > 790, the order is 32.3 x 105 > 389 x 102 > 0.079 x 104.
Correct Answer is :   32.3 x 105 > 389 x 102 > 0.079 x 104
Q4Choose the smallest number?

A. 5.81 × 10-4
B. 4.04 × 10-5
C. 5.81 × 10-5
D. 5.21 × 10-5

Solutions
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Step: 1
Order the exponents.
Step: 2
- 4 > - 5. So, 10 - 4 > 10 - 5
Step: 3
Compare numbers with the same exponent.
Step: 4
5.81 > 5.21 > 4.04
  [Comparing coefficients of 10 -5 .]
Step: 5
So, 5.81 × 10 -4 > 5.81 × 10 - 5 > 5.21 × 10 - 5 > 4.04 × 10 - 5
  [By using step 2.]
Step: 6
Therefore, the smallest number is 4.04 × 10 -5
  [By using step 2.]
Correct Answer is :   4.04 × 10-5
Q5Identify the largest number.

A. 7.21 × 10-5
B. 4.05 × 10-5
C. 6.81 × 10-4
D. 8.81 × 10-5

Solutions
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Step: 1
Order the exponents.
Step: 2
- 5 < - 4. So, 10 - 5 < 10 - 4.
Step: 3
Compare numbers with the same exponent.
Step: 4
4.05 < 7.21 < 8.81
  [Comparing co effiecient of 10 - 5.]
Step: 5
So, 4.05 × 10 - 5 < 7.21 × 10 -5 < 8.81 × 10 - 5 < 6.81 × 10 - 4
  [By using step 2.]
Step: 6
Therefore, the largest number is 6.81 × 10 - 4
Correct Answer is :   6.81 × 10-4
Q6Which among the following numbers is the largest?


A. 8.81 × 10-6
B. 5.05 × 10-6
C. 8.81 × 10-5
D. 8.21 × 10-6

Solutions
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Step: 1
Order the exponents.
Step: 2
- 6 < - 5. So, 10 - 6 < 10- 5
Step: 3
Compare numbers with the same exponent.
Step: 4
5.05 < 8.21 < 8.81
  [Comparing co efficient of 10 - 6.]
Step: 5
So, 5.05 × 10 - 6 < 8.21 × 10 - 6 < 8.81 × 10 - 6 < 8.81 × 10 - 5
  [By using step 2.]
Step: 6
Therefore, the largest number is 8.81 × 10 - 5
Correct Answer is :   8.81 × 10-5
Q7Identify the largest number.

A. 6.41 × 105
B. 6.41 × 104
C. 7.31 × 104
D. 7.91 × 103

Solutions
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Step: 1
Order the exponents.
Step: 2
3 < 4 < 5. So, 103 < 104 < 105.
Step: 3
Compare numbers with the same exponent
Step: 4
6.41 < 7.31
  [Comparing co efficient of 104.]
Step: 5
So, 7.91 × 103 < 6.41 × 104 < 7.31 × 104 < 6.41 × 10 5
  [By using step 2.]
Step: 6
Therefore, the largest number is 6.41 × 10 5
Correct Answer is :   6.41 × 105
Q8Which among the following numbers is the smallest?


A. 3.06 × 10-3
B. 5.71 × 10-3
C. 9.71 × 10-2
D. 4.11 × 10-3

Solutions
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Step: 1
Order the exponents.
Step: 2
- 3 < - 2
Step: 3
So, 10 - 3 < 10 - 2
Step: 4
Compare numbers with the same exponent.
Step: 5
3.06 < 4.11 < 5.71
  [Comparing co efficient of 10 - 3.]
Step: 6
So, 3.06 × 10 - 3 < 4.11 × 10 - 3 < 5.71 × 10 - 3 < 9.71 × 10 - 2
  [By using step2.]
Step: 7
Therefore, the smallest number is 3.06 × 10 - 3
Correct Answer is :   3.06 × 10-3
Q9Choose the largest number.


A. 4.05 × 10-5
B. 8.12 × 10-5
C. 9.72 × 10-5
D. 6.72 × 10-4

Solutions
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Step: 1
Order the exponents.
Step: 2
- 5 < - 4.
Step: 3
So, 10 - 5 < 10 - 4
Step: 4
Compare numbers with the same exponents.
Step: 5
4.05 < 8.12 < 9.72
  [Comparing co efficient of 10 - 5]
Step: 6
So, 4.05 × 10 - 5 < 8.12 × 10 - 5 < 9.72 × 10 - 5 < 6.72 × 10 - 4
  [By using step 2.]
Step: 7
Therefore, the largest number is 6.72 × 10- 4
Correct Answer is :   6.72 × 10-4
Q10Identify the smallest number.


A. 9.91 × 103
B. 9.31 × 104
C. 8.41 × 104
D. 8.41 × 105

Solutions
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Step: 1
order the exponents.
Step: 2
3 < 4 < 5
Step: 3
So, 103 < 104 < 105
Step: 4
Compare numbers with the same exponents.
Step: 5
8.41 < 9.31
  [Comparing co efficients of 104)
Step: 6
So, 9.91 × 103 < 8.41 × 104 < 9.31 × 104 < 8.41 × 105
  [By using step 2.]
Step: 7
Therefore, the smallest number is 9.91 × 103
Correct Answer is :   9.91 × 103

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