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Scientific Notation Worksheets - Page 14

Scientific Notation Worksheets
  • Page 14
 131.  
A hydrogen atom has a mass of 1.67 × 10-27 kilogram. Express the mass of 4 × 102 hydrogen atoms in scientific notation.
a.
6.68 x 10-25 kilogram
b.
6.68 x 1029 kilogram
c.
6.68 x 10-29 kilogram
d.
6.68 x 1025 kilogram


Solution:

The mass of a hydrogen atom is 1.67 x 10-27 kilogram.

The mass of 4 x 102 hydrogen atoms is (1.67 x 10-27 ) x (4 x 102)

= (1.67 x 4) x (10-27 x 102) kilogram
[Use commutative property of multiplication.]

= 6.68 x (10-27 x 102) kilogram
[Multiply 1.67 and 4.]

= 6.68 x 10-25 kilogram
[Add the exponents.]


Correct answer : (1)
 132.  
The weight of an elephant is 1600 kgs. Write the number in scientific notation.
a.
1.6 x 103
b.
16 x 10-3
c.
1.6
d.
1.6 x 104


Solution:

A number is expressed in scientific notation as the product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.

The first factor is 1.6.
[Move the decimal point such that the number is greater than 1 but less than 10.]

The second factor is 103.
[As the decimal is moved 3 places to the left, take the exponent of 10 as 3.]

So, the number 1600 in scientific notation is 1.6 x 103.


Correct answer : (1)
 133.  
Order the numbers 130 × 102, 16.3 × 105, 0.061 × 104 from the greatest to the least.
a.
130 x 102 > 16.3 x 105 > 0.061 x 104
b.
0.061 x 104 > 16.3 x 105 > 130 x 102
c.
16.3 x 105 > 130 x 102 > 0.061 x 104
d.
None of the above


Solution:

130 x 102 = 1.30 x 102 x 102
[Write 130 as 1.30 x 102.]

= 1.30 x 104
[Add the exponents.]

= 13000
[Simplify.]

16.3 x 105 = 1.63 x 101 x 105
[Write 16.3 as 1.63 x 101.]

= 1.63 x 106
[Add the exponents.]

= 1630000
[Simplify.]

0.061 x 104 = 6.100 x 10-2 x 104
[Write 0.061 as 6.100 x 10-2.]

= 6.100 x 102
[Add the exponents.]

= 610
[Simplify.]

Since 1630000 > 13000 > 610, the order is 16.3 x 105 > 130 x 102 > 0.061 x 104.


Correct answer : (3)
 134.  
In _______ notation, we change expressions from scientific notation by simplifying the product of two factors.
a.
Exponential
b.
Standard
c.
Scientific
d.
Algebric


Solution:

We change expressions from scientific notation to standard notation by simplifying the product of two factors.


Correct answer : (2)
 135.  
Multiply 5 × 106 and 6 × 10-3. Express the result in scientific notation.
a.
3
b.
3 x 103
c.
3 x 104
d.
30


Solution:

= 5 x 6 x 106 x 10-3
(5 x 106 ) x (6 x 10-3 )
[Use commutative property of multiplication.]

= 30 x 106 x 10-3
[Multiply 5 and 6.]

= 30 x 103
[Add exponents.]

= 3 x 101 x 103
[Write 30 = 3 x 101 in scientific notation.]

= 3 x 104
[Add exponents.]


Correct answer : (3)
 136.  
Find the values of a and b in the table.
3 x 1013 x 1030
3 x 1003 x 13
3 x 10-23 x ab
a.
0.01, 0.03
b.
1.00, 3.00
c.
0.10, 0.30
d.
None of the above


Solution:

3 x 10-2 = 3 x 1/102
[Write as a positive exponent.]

= 3 x 1100 = 3 x 0.01

= 0.03

The value of a is 0.01 and the value of b is 0.03.


Correct answer : (1)
 137.  
Find the values of a and b in the table.
2 x 1022 x 100200
2 x 1002 x ab
a.
a = 2, b = 1
b.
a = 1, b = 2
c.
a = 1, b = 3
d.
a = 2, b = 3


Solution:

2 x 100 = 2 x 1 = 2

The value of a is 1 and b is 2.


Correct answer : (2)
 138.  
Write 29000 in scientific notation.
a.
2.9 × 105
b.
2.9 × 103
c.
2.9 × 104
d.
None of the above


Solution:

A number in scientific notation is represented as a product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.

The first factor in the scientific notation of 29000 is 2.9.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 104.
[The decimal point is moved 4 places to the left. Use this number as the exponent of 10.]

So, the scientific notation of 29000 is 2.9 × 104.


Correct answer : (3)
 139.  
Write 310000000 in scientific notation.
a.
3.1 × 108
b.
3.1 × 109
c.
3.1 × 107
d.
3.1 × 106


Solution:

A number in scientific notation is a product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.

The first factor in the scientific notation of 310000000 is 3.1.
[Move the decimal point to get a factor greater than 1 and less than 10.]

The second factor is 108 .
[The decimal point moved 8 places to the left. Use this number as the exponent of 10.]

So, the scientific notation of 310000000 is 3.1 × 108.


Correct answer : (1)
 140.  
The speed of sound in air is 331 m/s at 0oC. Write the speed of sound in air in scientific notation.
a.
3.31 x 101
b.
3.31 x 103
c.
3.31 x 102
d.
None of the above


Solution:

A number in scientific notation is a product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.

The first factor in the scientific notation of 331 is 3.31
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 102
[The decimal point is moved 2 places to the left. Use this number as the exponent of 10.]

The speed of sound in air in scientific notation is 3.31 x 102 m/s.


Correct answer : (3)

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