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Scientific Notation Worksheets - Page 8

Scientific Notation Worksheets
  • Page 8
 71.  
Choose the scientific notation of 0.00023.
a.
2.3 × 10- 3
b.
2.3 × 104
c.
2.3 × 10- 5
d.
2.3 × 10- 4


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 0.00023 is 2.3.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 10- 4.
[The decimal point moved 4 places to the right. The negative of this number is used as the exponent of 10.]

The scientific notation of the number is 2.3 × 10- 4.


Correct answer : (4)
 72.  
The annual rainfall in Alabama is about 0.000898 mi. Identify the scientific form.
a.
8.98 × 10-4
b.
8.98 × 10-5
c.
8.98 × 10-3
d.
8.98 × 104


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 0.000898 is 8.98.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 10-4.
[The decimal point moved 4 places to the right. The negative of this number is used as the exponent of 10.]

The annual rainfall in Alabama expressed in scientific notation is 8.98 × 10-4 mi.


Correct answer : (1)
 73.  
Identify the scientific notation of 0.000003.
a.
3 × 10-4
b.
3 × 10-7
c.
3 × 10-6
d.
3 × 10-5


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 0.000003 is 3.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 10-6.
[The decimal point moved 6 places to the right. The negative of this number is used as the exponent of 10.]

The scientific notation of the number is 3 × 10-6.


Correct answer : (3)
 74.  
The weight of a book was 0.0035 pounds. Identify the scientific notation for this number.
a.
3.5 × 10-2
b.
3.5 × 10-3
c.
3.5 × 10-4
d.
3.5 × 10-5


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 0.0035 is 3.5.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

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

The weight of the book in scientific notation is 3.5 × 10 -3 pounds.


Correct answer : (2)
 75.  
The radius of a circle is 0.003 meters. Identify this number in scientific notation.
a.
3 × 10- 4 meters
b.
3 × 10- 2 meters
c.
3 × 10- 3 meters
d.
3 × 10- 5 meters


Solution:

A number in scientific notation is represented 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 in the scientific notation of 0.003 is 3.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 10- 3.
[The decimal point is moved 3 places to the right. The negative of this number is used as the exponent of 10.]

The radius of the circle in scientific notation is 3 × 10- 3 meters.


Correct answer : (3)
 76.  
The ratio of the mass of the planet Mercury to that of the Earth is 0.0553. Choose the standard form.
a.
5.53 × 10-3
b.
5.53 × 10-4
c.
5.53 × 10-2
d.
5.53 × 10-1


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 0.0553 is 5.53.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 10-2.
[The decimal point moved 2 places to the right. The negative of this number is used as the exponent of 10.]

Expressed in scientific notation, the ratio of mass of Mercury to that of Earth is 5.53 × 10-2.


Correct answer : (3)
 77.  
Choose the standard form of 3.3 × 10-4.
a.
0.00033
b.
0.033
c.
0.000033
d.
0.0033


Solution:

3.3 × 10-4 = 0.00033
[Multiplying by 0.0001 moves the decimal point 4 places to the left.]

The standard form of 3.3 × 10-4 is 0.00033.


Correct answer : (1)
 78.  
The diameter of a cable is 3.73 × 10-3 meters. Identify the standard form.
a.
0.000373
b.
0.373
c.
0.0373
d.
0.00373


Solution:

3.73 × 10-3 = 0.00373
[Multiplying by 0.001 moves the decimal point 3 places to the left.]

The diameter of the cable in standard notation is 0.00373 meters.


Correct answer : (4)
 79.  
Express 4 × 10- 3 in standard notation.
a.
0.004
b.
0.0004
c.
0.04
d.
0.00004


Solution:

4 × 10-3 = 0.004
[Multiplying by 0.001 moves the decimal point 3 places to the left.]

The standard form of 4 × 10-3 is 0.004.


Correct answer : (1)
 80.  
The area of square ABCD is 2 × 10-2 square meter. Express the number in standard form.
a.
0.02
b.
0.2
c.
0.002
d.
2


Solution:

2 × 10-2 = 0.02
[Multiplying by 0.01 moves the decimal point 2 places to the left.]

The area of square ABCD in standard form is 0.02 m2.


Correct answer : (1)

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