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.

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.

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.

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.

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.

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.

77.
Choose the standard form of 3.3 × 10-4.
 a. 0.00033 b. 0.033 c. 3.3e-05 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.

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.

79.
Express 4 × 10- 3 in standard notation.
 a. 0.004 b. 0.0004 c. 0.04 d. 4e-05

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.

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.