﻿ Scientific Notation Worksheets - Page 12 | Problems & Solutions

# Scientific Notation Worksheets - Page 12

Scientific Notation Worksheets
• Page 12
111.
One meter is equal to 100 centimeters. Identify this number in scientific notation.
 a. 1 x 101 cm b. 1 x 103 cm c. 1 x 102 cm 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 100 is 1
[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.]

100 centimeters in scientific notation is 1 x 102 centimeters.

112.
One mean solar day is equal to 86400 mean solar seconds. Identify this number in scientific notation.
 a. 8.64 x 103 b. 8.64 x 105 c. 8.64 x 104 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 86400 is 8.64
[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.]

One Mean Solar Day in scientific notation is equal to 8.64 x 104 Mean Solar Seconds.

113.
Identify 5.2 × 103 in standard form.
 a. 5.2 b. 5200 c. 520 d. 52000

#### Solution:

5.2 × 103 = 5200
[Multiplying by 1000 moves the decimal point 3 places to the right.]

The standard form of 5.2 × 103 is 5200.

114.
Identify 5.619 × 108 in standard form.
 a. 561900000 b. 5619000000 c. 56190000 d. None of the above

#### Solution:

5.619 × 108 = 561900000
[Multiplying by 100000000 moves the decimal point 8 places to the right.]

The standard form of 5.619 × 108 is 561900000.

115.
The total area occupied by South Carolina is about 3.2 × 104 square miles. Identify the number in standard form.
 a. 32,000 b. 320,000 c. 320 d. 3,200

116.
The total men in the Civilian Labor Force in the U.S. in the year 2001 was about 7.5743 x 107. Identify this number written in standard form.
 a. 7,57,430 b. 7,574,300 c. 75,743,000 d. None of the above

#### Solution:

7.5743 x 107 = 75,743,000
[Multiplying by 10,000,000 moves the decimal point 7 places to the right.]

The total men Civilian Labor Force in the standard form is 75,743,000.

117.
One kilogram is equal to 1 × 103 grams. Identify this number in standard form.
 a. 1000 gm b. 100 gm c. 10 gm d. None of the above

#### Solution:

1 × 103 = 1000
[Multiplying by 1000 moves the decimal point 3 places to the right.]

The representation of 1 × 103 in standard form is 1000 gm.

118.
The total number of cellular phone subscribers in the U.S. in the year 2000 was about 1.1 × 108. Identify this number in standard form.
 a. 11,100,000 b. 11,000,000 c. 111,000,000 d. 110,000,000

#### Solution:

1.1 × 108 = 110,000,000
[Multiplying by 100,000,000 moves the decimal point 8 places to the right.]

The total number of Cellular Phone Subscribers in standard form is 110,000,000.

119.
Write 0.00002 in scientific notation.
 a. 2 b. 2 × 10-5 c. 2 × 106 d. 2 × 105

#### Solution:

A number is expressed in scientific notation 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 0.00002 is 2.
[Move decimal point 5 places to the right to get a factor between 1 and 10.]

The second factor is 10-5.
[As the decimal point is moved 5 places to the right, take exponent of 10 as - 5.]

So, the scientific notation of 0.00002 is 2 × 10-5.

120.
Identify 434 × 10-2 in standard form.
 a. 4340 b. 43.4 c. 4.34 d. 434

#### Solution:

As the exponent of 10 in the number is - 2, move the decimal point 2 places to the left.

So, the number in standard form is 4.34.
[Move decimal point 2 places to the left.]