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Scientific Notation Worksheets
• Page 20
191.
Express 7.6 × 10- 5 in standard form. a. 7.6e-06 b. 7.6e-05 c. 0.00076 d. 0.0076

#### Solution:

7.6 × 10- 5 = 0.000076
[Since the exponent of 10 is - 5, move the decimal point 5 places to the left.]

So, the decimal form of 7.6 × 10- 5 is 0.000076.

Correct answer : (2)
192.
Rewrite the number 0.00006 using scientific notation. a. 0.6 × 10- 5 b. 6 × 105 c. 6 × 10- 4 d. 6 × 10- 5

#### 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 0.00006 is 6.
[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 0.00006 is 6 × 10- 5.

Correct answer : (4)
193.
Express 4,000,000 in scientific notation. a. 4 × 107 b. 4 × 105 c. 4 d. 4 × 106

#### Solution:

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

The first factor is 4.
[Move the decimal point 6 places to the left to get a number between 1 and 10.]

The second factor is 106.
[As the decimal is moved 6 places to the right, take 6 as exponent of 10.]

So, 4,000,000 can be written in scientific notation as 4 × 106.

Correct answer : (4)
194.
Simplify and write the result in scientific notation. a. 0.2 × 107 b. 2.0 × 104 c. 2.0 × 108 d. 2.0 × 107

#### Solution:

0.66×1043.3×10- 4 = (0.66 / 3.3) × 10410- 4
[Write as a product.]

= 0.2 × (108)
[Use quotient of powers property.]

= (2.0 × 10- 1) × 108
[Write 0.2 in scientific notation.]

= 2.0 × 107
[Use product of powers property.]

Correct answer : (4)
195.
Simplify and write the result in scientific notation. a. 3.3 × 106 b. 3.3 × 10- 6 c. - 3.3 × 106 d. - 3.3 × 10- 6

#### Solution:

2.0×10- 96×10- 4 = (2.0 / 6) × 10- 910- 4
[Write as a product.]

= 0.33 × 10- 5
[Use quotient of powers property.]

= (3.3 × 10- 1) × 10- 5
[Write 0.33 in scientific notation.]

= 3.3 × 10- 6
[Use product of powers property.]

Correct answer : (2)
196.
The mean distance of the Earth from the Moon is about 384,400 km. Write the distance in scientific notation. a. 1.922 × 105 km b. 3.844 × 105 km c. 3844 km d. 0.3844 × 105 km

#### 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 × 105 km.

Correct answer : (2)
197.
The total men in the Civilian Labor Force in the U.S in the year 2001 was about 7.5743 × 107. Write the number in decimal form. a. 7,574,300 b. 757,430 c. 75,743,000 d. 757,430,000

#### Solution:

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

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

Correct answer : (3)
198.
Multiply 7 × 107 and 5 × 10- 2. Express the result in scientific notation. a. 3.5 × 106 b. 3.5 c. 35 d. 3.5 × 105

#### Solution:

= 7 × 5 × 107 × 10- 2
(7 × 107 ) × (5 × 10- 2 )
[Use commutative property of multiplication.]

= 35 × 107 × 10- 2
[Multiply 7 and 5.]

= 35 × 105
[Add exponents.]

= 3.5 × 101 × 105
[Write 35 = 3.5 × 101 in scientific notation.]

= 3.5 × 106
[Add exponents.]

Correct answer : (1)
199.
Express 760,000,000,000 in scientific notation. a. 7.6 × 109 b. 7.6 × 108 c. 7.6 × 1011 d. 7.6 × 1010

#### Solution:

760,000,000,000
[Move the decimal point 11 places to the left, to get a factor greater than or equal to 1 and less than 10.]

= 7.6 × 100,000,000,000

= 7.6 × 1011
[The exponent of 10 is 11.]

The scientific notation of the number 760,000,000,000 is 7.6 × 1011.

Correct answer : (3)

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