﻿ Scientific Notation Worksheets - Page 18 | Problems & Solutions

# Scientific Notation Worksheets - Page 18

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.

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.]

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.

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.

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.

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.

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.

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

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

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.

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.