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Scientific Notation Worksheets
• Page 18
171.
The military expenditure of a country is about 1.78 × 109 dollars per year. Write this number in standard form. a. 1,780,000,000 dollars per year b. 17,800,000 dollars per year c. 178 dollars per year d. 1,780 dollars per year

#### Solution:

1.78 x 109 = 1,780,000,000 acres
[Multiplying by 1,000,000,000 moves the decimal point 9 places to the right.]

The total military expenditure of the country in standard form is 1,780,000,000 dollars per year.

Correct answer : (1)
172.
Solve the expression (7.3 × 109)(4.8 × 109) and express the result in scientific notation. a. 3.504 b. 3.504 × 1017 c. 3.504 × 1019 d. 3.504 × 1018

#### Solution:

(7.3 × 109)(4.8 × 109) = (7.3 × 4.8)(109 × 109)
[Use multiplication properties.]

= 35.04 × 1018
[Use product of powers property.]

= (3.504 × 101) × 1018
[Write 35.04 in scientific notation.]

= 3.504 × 1019
[Use product of powers property.]

Correct answer : (3)
173.
The total number of farms in the year 2000 in the U.S was about 1,432,000. Write the number in scientific notation. a. 1.432 × 107 b. 1.432 × 106 c. 1.432 × 104 d. 1.432 × 105

#### 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 1,432,000 is 1.432.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 106.
[The decimal point is moved 6 places to the left. Use this number as the exponent of 10.]

The total number of farms in scientific notation is 1.432 × 106.

Correct answer : (2)
174.
The Orbital Period of the planet Pluto is about 9.1 × 104 days. Write the number in decimal form. a. 9,100 days b. 910,000 days c. 9,100,000 days d. 91,000 days

#### Solution:

9.1 × 104 = 91,000
[Multiplying by 10,000, moves the decimal point 4 places to the right.]

The Orbital Period of the planet Pluto in decimal form is 91,000 days.

Correct answer : (4)
175.
The height of the Empire State building in New York is 1,250 ft. Write this number in scientific notation.  a. 1.25 × 104 b. 1.25 × 103 c. 0.125 × 103 d. 1.25 × 102

#### Solution:

A number in scientific notation is written as the product of two factors. The first factor is an integer between 1 to 10 and the second factor is an exponent of 10.

The first factor in the scientific notation of 1,250 is 1.25.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 103.
[The decimal is moved to 3 places to the left. Use this number as the exponent of 10.]

So, the height of the Empire state building written in scientific notation is 1.25 × 103.

Correct answer : (2)
176.
The mass of Earth is about 5.976 × 1024 kg. Write this number in decimal form. a. 5,976,000,000,000,000,000,000,000 b. 59,760,000,000,000,000,000,000,000 c. 5,976,000,000,000 d. 597,600,000,000,000,000,000,000

#### Solution:

5.976 × 1024 = 5,976,000,000,000,000,000,000,000
[A positive exponent indicates a large number. Move the decimal point 24 places to the right.]

= 5,976,000,000,000,000,000,000,000

The mass of Earth written in the decimal form is 5,976,000,000,000,000,000,000,000 kg.

Correct answer : (1)
177.
A teacher asked four students for the value of 5 × 105, Ed said 50,000, Andy said 500,000, Tommy said 5,000,000 and Tim said 50,000,000. Who among the four is correct? a. Ed b. Tim c. Andy d. Tommy

#### Solution:

5 × 105 = 5 × 100,000
[Evaluate power.]

= 500,000
[Multiply 5 and 100,000.]

So, Andy is correct.

Correct answer : (3)
178.
A hydrogen atom has a mass of 1.67 × 10- 27 kilogram. Express the mass of 3 × 102 hydrogen atoms in scientific notation. a. 5.01 × 1025 kilogram b. 5.01 × 10- 29 kilogram c. 5.01 × 1029 kilogram d. 5.01 × 10- 25 kilogram

#### Solution:

The mass of a hydrogen atom is 1.67 × 10- 27 kilogram.

The mass of 3 × 102 hydrogen atoms is (1.67 × 10-27 ) × (3 × 102).

= (1.67 × 3) × (10- 27 × 102)
[Use commutative property of multiplication.]

= 5.01 × (10- 27 × 102)
[Multiply 1.67 and 3.]

= 5.01 × 10- 25
[Add the exponents.]

The mass of 3 × 102 hydrogen atoms in scientific notation is 5.01 × 10- 25 kilogram.

Correct answer : (4)
179.
Radius of the Sun is about 695,000 km. Write this number in scientific notation. a. 6.95 × 105 km b. 6.95 × 104 km c. 6.95 × 106 km d. 6.95 × 103 km

#### Solution:

A number in scientific notation is written as the product of two factors. The first factor is an integer between 1 to 10 and the second factor is an exponent of 10.

The first factor in the scientific notation of 695,000 is 6.95.
[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 is moved 5 places to the left. Use this number as the exponent of 10.]

So, radius of the Sun in scientific notation is 6.95 × 105 km.

Correct answer : (1)
180.
The mean distance from Pluto to the Sun is about 5,913,520,000 km. Write this number in scientific notation. a. 5.91352 × 107 km b. 5.91352 × 1010 km c. 5.91352 × 109 km d. 5.91352 × 108 km

#### Solution:

A number in scientific notation is written as the product of two factors. The first factor is an integer between 1 to 10 and the second factor is an exponent of 10.

The first factor in the scientific notation of 5,913,520,000 is 5.91352.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 109.
[The decimal is moved 9 places to the left. Use this number as the exponent of 10.]

So, the mean distance from Pluto to the Sun written in scientific notation is 5.91352 × 109 km.

Correct answer : (3)

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