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Scientific Notation Worksheets
• Page 19
181.
The mean distance from Venus to the Sun is about 1.08 × 109 km. Write this number in decimal form. a. 180,000,000 km b. 1,080,000,000 km c. 108,000,000 km d. 18,000,000 km

#### Solution:

1.08 × 109 = 1,080,000,000 km
[Multiplying by 1,000,000,000 moves the decimal point 9 places to the right.]

The mean distance from Venus to the Sun expressed in decimal form is 1,080,000,000 km.

Correct answer : (2)
182.
The total extent of farm land in U.S is about 9.87 × 108 acres. Write this number in decimal form. a. 9,870,000 acres b. 989,000,000 acres c. 987,000,000 acres d. 978,000,000 acres

#### Solution:

9.87 × 108 = 987,000,000 acres
[Multiplying by 100,000,000 moves the decimal point 8 places to the right.]

The total extent of farm land expressed in decimal form is 987,000,000 acres.

Correct answer : (3)
183.
The lowest temperature in a lab setting is about 2.8 × 10 - 10 ok. Write this number in decimal form. a. 0.0000000028 ok b. 0.000000028 ok c. 0.000000000028 ok d. 0.00000000028 ok

#### Solution:

2.8 × 10 - 10 = 0.00000000028
[Multiplying by 0.0000000001 moves the decimal point 10 places to the left.]

The lowest temperature in a lab setting expressed in decimal form is 0.00000000028 ok.

Correct answer : (4)
184.
Simplify the product (7.6 × 108) (6.3 × 10-3) and write the result in scientific notation. a. 4.788 × 105 b. 4.788 × 106 c. 47.880 × 106 d. 4.788

#### Solution:

(7.6 × 108) (6.3 × 10-3) = (7.6 × 6.3) (108 × 10-3)
[Use multiplication properties.]

= (47.88) (105)
[Use product of powers property.]

= (4.788 × 101) × 105
[Write 47.88 in scientific notation.]

= 4.788 × 106
[Use product of powers property.]

Correct answer : (2)
185.
Simplify:
(4 × 10- 9)2 a. 1.6 × 10- 18 b. 16 × 10- 1 c. 16 × 1018 d. 1.6 × 10- 17

#### Solution:

(4 × 10- 9)2 = 42 × (10- 9)2
[Use power of a product property.]

= 16 × 10-18
[Use power of a power property.]

= (1.6 × 101) × 10- 18
[Write 16 in scientific notation.]

= 1.6 × 10- 17
[Use product of powers property.]

Correct answer : (4)
186.
Write 950,000,000 in scientific notation. a. 9.5 × 108 b. 9.5 × 106 c. 9.5 × 107 d. 9.5 × 109

#### Solution:

A number in scientific notation is 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 950,000,000 is 9.5.
[Move the decimal point to get a factor greater than 1 and less than 10.]

The second factor is 108.
[The decimal point moved 8 places to the left. Use this number as the exponent of 10.]

So, the scientific notation of 950,000,000 is 9.5 × 108.

Correct answer : (1)
187.
The speed of sound in air is 331 m/s at 0oC. Write the speed of sound in air in scientific notation. a. 3.31 × 101 m/s b. 0.331 × 102 m/s c. 3.31 × 102 m/s d. 3.31 × 103 m/s

#### Solution:

A number in scientific notation is 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 331 is 3.31.
[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.]

The speed of sound in air in scientific notation is 3.31 × 102 m/s.

Correct answer : (3)
188.
The total area occupied by the state of South Carolina is about 3.2 × 104 square miles. Write the number in decimal form. a. 3,200 square miles b. 32,000 square miles c. 3,200,000 square miles d. 320,000 square miles

#### Solution:

3.2 × 104 = 32,000
[Multiplying by 10,000, moves the decimal point 4 places to the right.]

The total area occupied by the state of South Carolina in decimal form is 32,000 square miles.

Correct answer : (2)
189.
Express 333 × 10 - 3 in decimal form. a. 333 b. 33.3 c. 0.333 d. 3.33

#### Solution:

As the exponent of 10 in the number is - 3, move the decimal point 3 places to the left.

So, the number in decimal form is 0.333.

Correct answer : (3)
190.
Express 9.673 × 106 in standard form. a. 967,300 b. 96,730 c. 96,730,000 d. 9,673,000

#### Solution:

As the exponent of 10 in the number is 6, move the decimal point 6 places to the right.

9.673 × 106 = 9,673,000
[As there are only 3 digits after the decimal, insert 3 zeroes at the end.]

Correct answer : (4)

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