Scientific Notation Worksheets

**Page 19**

181.

The mean distance from Venus to the Sun is about 1.08 × 10^{9} 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 |

[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 × 10^{8} 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 |

[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} ^{o}k. Write this number in decimal form.

a. | 0.0000000028 ^{o}k | ||

b. | 0.000000028 ^{o}k | ||

c. | 0.000000000028 ^{o}k | ||

d. | 0.00000000028 ^{o}k |

[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

Correct answer : (4)

184.

Simplify the product (7.6 × 10^{8}) (6.3 × 10^{-3}) and write the result in scientific notation.

a. | 4.788 × 10 ^{5} | ||

b. | 4.788 × 10 ^{6} | ||

c. | 47.880 × 10 ^{6} | ||

d. | 4.788 |

[Use multiplication properties.]

= (47.88) (10

[Use product of powers property.]

= (4.788 × 10

[Write 47.88 in scientific notation.]

= 4.788 × 10

[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 × 10 ^{18} | ||

d. | 1.6 × 10 ^{- 17} |

[Use power of a product property.]

= 16 × 10

[Use power of a power property.]

= (1.6 × 10

[Write 16 in scientific notation.]

= 1.6 × 10

[Use product of powers property.]

Correct answer : (4)

186.

Write 950,000,000 in scientific notation.

a. | 9.5 × 10 ^{8} | ||

b. | 9.5 × 10 ^{6} | ||

c. | 9.5 × 10 ^{7} | ||

d. | 9.5 × 10 ^{9} |

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 10

[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 × 10

Correct answer : (1)

187.

The speed of sound in air is 331 m/s at 0^{o}C. Write the speed of sound in air in scientific notation.

a. | 3.31 × 10 ^{1} m/s | ||

b. | 0.331 × 10 ^{2} m/s | ||

c. | 3.31 × 10 ^{2} m/s | ||

d. | 3.31 × 10 ^{3} m/s |

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 10

[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 × 10

Correct answer : (3)

188.

The total area occupied by the state of South Carolina is about 3.2 × 10^{4} 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 |

[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 |

So, the number in decimal form is 0.333.

Correct answer : (3)

190.

Express 9.673 × 10^{6} in standard form.

a. | 967,300 | ||

b. | 96,730 | ||

c. | 96,730,000 | ||

d. | 9,673,000 |

9.673 × 10

[As there are only 3 digits after the decimal, insert 3 zeroes at the end.]

Correct answer : (4)