Scientific Notation Worksheets

**Page 18**

171.

The military expenditure of a country is about 1.78 × 10^{9} 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 |

[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 × 10^{9})(4.8 × 10^{9}) and express the result in scientific notation.

a. | 3.504 | ||

b. | 3.504 × 10 ^{17} | ||

c. | 3.504 × 10 ^{19} | ||

d. | 3.504 × 10 ^{18} |

[Use multiplication properties.]

= 35.04 × 10

[Use product of powers property.]

= (3.504 × 10

[Write 35.04 in scientific notation.]

= 3.504 × 10

[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 × 10 ^{7} | ||

b. | 1.432 × 10 ^{6} | ||

c. | 1.432 × 10 ^{4} | ||

d. | 1.432 × 10 ^{5} |

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 10

[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 × 10

Correct answer : (2)

174.

The Orbital Period of the planet Pluto is about 9.1 × 10^{4} days. Write the number in decimal form.

a. | 9,100 days | ||

b. | 910,000 days | ||

c. | 9,100,000 days | ||

d. | 91,000 days |

[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 × 10 ^{4} | ||

b. | 1.25 × 10 ^{3} | ||

c. | 0.125 × 10 ^{3} | ||

d. | 1.25 × 10 ^{2} |

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 10

[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 × 10

Correct answer : (2)

176.

The mass of Earth is about 5.976 × 10^{24} 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 |

[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 × 10^{5}, 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 |

[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 × 10^{2} hydrogen atoms in scientific notation.

a. | 5.01 × 10 ^{25} kilogram | ||

b. | 5.01 × 10 ^{- 29} kilogram | ||

c. | 5.01 × 10 ^{29} kilogram | ||

d. | 5.01 × 10 ^{- 25} kilogram |

The mass of 3 × 10

= (1.67 × 3) × (10

[Use commutative property of multiplication.]

= 5.01 × (10

[Multiply 1.67 and 3.]

= 5.01 × 10

[Add the exponents.]

The mass of

Correct answer : (4)

179.

Radius of the Sun is about 695,000 km. Write this number in scientific notation.

a. | 6.95 × 10 ^{5} km | ||

b. | 6.95 × 10 ^{4} km | ||

c. | 6.95 × 10 ^{6} km | ||

d. | 6.95 × 10 ^{3} km |

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 10

[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 × 10

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 × 10 ^{7} km | ||

b. | 5.91352 × 10 ^{10} km | ||

c. | 5.91352 × 10 ^{9} km | ||

d. | 5.91352 × 10 ^{8} km |

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 10

[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 × 10

Correct answer : (3)