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Scientific Notation Worksheets - Page 11

Scientific Notation Worksheets
  • Page 11
 101.  
Find the standard form of 6.32 × 10-5.
a.
632,000
b.
632 × 10-7
c.
0.0000632
d.
0.00000632


Answer: (c)


Correct answer : (3)
 102.  
The radius of a Hydrogen atom is equal to 1 × 10-1 angstrom. Write this number in standard form.
a.
0.01
b.
0.001
c.
0.0001
d.
0.1


Solution:

1 x 10-1 = 0.1
[A negative exponent indicates a small number. Move the decimal point 1 place to the left.]

The radius of a Hydrogen atom in standard form is 0.1 angstrom.


Correct answer : (4)
 103.  
The viscosity of ethanol at 30oc is 1 × 10- 3 NSM- 2. Write this number in standard form.
a.
0.01
b.
0.1
c.
0.0001
d.
0.001


Solution:

1 x 10-3 = 0.001
[A negative exponent indicates a small number. Move the decimal point 3 places to the left]

= 0.001
[10-3 = 1 / 1000= 0.001]

The viscosity of ethanol at 30oc is 0.001 NSM-2.


Correct answer : (4)
 104.  
What is the value of n, if 0.00023 = 2.3 × 10n?
a.
- 6
b.
- 5
c.
- 4
d.
- 3


Solution:

0.00023 = 2.3 × 10 - 4
[Move the decimal point 4 places to the right to get a factor greater than or equal to 1 and less than 10.]

2.3 × 10 - 4 = 2.3 × 10n
[Substitute the value of 0.00023 = 2.3 × 10- 4.]

Since the two factors are equal, the exponents of 10 are equal.

The value of n = - 4.


Correct answer : (3)
 105.  
Which of the following is equivalent to 2.2 × 10- 3?
a.
0.022
b.
0.22
c.
0.0022
d.
0.00022


Solution:

2.2 × 10-3 = 0.0022
[A negative exponent indicates a small number. Move the decimal point 3 places to the left.]

From the choices, the choice C is equivalent to the expression.


Correct answer : (3)
 106.  
Arrange the numbers 70, 77, 75, 79 from the least to the greatest.
a.
70, 77, 79, 75
b.
75, 70, 79, 77
c.
79, 70, 77, 75
d.
70, 75, 77, 79


Solution:

0 < 5 < 7 < 9
[Order the exponents.]

So, 70 < 75 < 77 < 79.

The order of the numbers from least to highest is 70, 75, 77, 79.


Correct answer : (4)
 107.  
The mean distance of the Earth from the Moon is about 384,400 km. Write this number in scientific notation.

a.
3.844 x 107
b.
3.844 x 106
c.
3.844 x 105
d.
None of the above


Solution:

A number in scientific notation is 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 in the scientific notation of 384,400 is 3.844
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 105
[The decimal point is moved 5 places to the left. Use this number as the exponent of 10.]

The mean distance of the Earth from the Moon in scientific notation is about 3.844 x 105 km.


Correct answer : (3)
 108.  
An area of 6800 m2 in the State of Texas is covered with water. Write this number in scientific notation.
a.
6.8 x 104
b.
6.8 x 103
c.
6.8 x 102
d.
None of the above


Solution:

A number in scientific notation is 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 in the scientific notation of 6800 is 6.8
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 103
[The decimal point is moved 3 places to the left. Use this number as the exponent of 10.]

The area covered with water in the state of Texas in scientific notation is 6.8 x 103 m2.


Correct answer : (2)
 109.  
Write 62 1000000 in scientific notation.
a.
6.2 x 10-4
b.
6.2 x 10-3
c.
6.2 x 10-5
d.
6.2 x 10-6


Solution:

621000000 = 0.000062
[Write in decimal form.]

= 6.2 x 0.00001
[Move the decimal point 5 places to the right, to get a factor greater than or equal to 1 and less than 10.]

= 6.2 x 10-5
[The exponent of 10 is -5.]

The scientific notation of 62 / 1000000 is 6.2 x 10-5


Correct answer : (3)
 110.  
The total number of farms in the year 2000 in the U.S. was about 1,423,000. Write this number in scientific notation.
a.
1.423 x 107
b.
1.423 x 105
c.
1.423 x 106
d.
None of the above


Solution:

A number in scientific notation is 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 in the scientific notation of 1,423,000 is 1.423
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 106
[The decimal point is moved 6 places to the left. Use this number as the exponent of 10.]

The total number of farms in scientific notation is 1.423 x 106.


Correct answer : (3)

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