Scientific Notation Worksheets

**Page 20**

191.

Express 7.6 × 10^{- 5} in standard form.

a. | 0.0000076 | ||

b. | 0.000076 | ||

c. | 0.00076 | ||

d. | 0.0076 |

[Since the exponent of 10 is - 5, move the decimal point 5 places to the left.]

So, the decimal form of 7.6 × 10

Correct answer : (2)

192.

Rewrite the number 0.00006 using scientific notation.

a. | 0.6 × 10 ^{- 5} | ||

b. | 6 × 10 ^{5} | ||

c. | 6 × 10 ^{- 4} | ||

d. | 6 × 10 ^{- 5} |

The first factor in the scientific notation of 0.00006 is 6.

[Move decimal point 5 places to the right to get a factor between 1 and 10.]

The second factor is 10

[As the decimal point is moved 5 places to the right, take exponent of 10 as - 5.]

So, the scientific notation of 0.00006 is 6 × 10

Correct answer : (4)

193.

Express 4,000,000 in scientific notation.

a. | 4 × 10 ^{7} | ||

b. | 4 × 10 ^{5} | ||

c. | 4 | ||

d. | 4 × 10 ^{6} |

The first factor is 4.

[Move the decimal point 6 places to the left to get a number between 1 and 10.]

The second factor is 10

[As the decimal is moved 6 places to the right, take 6 as exponent of 10.]

So, 4,000,000 can be written in scientific notation as 4 × 10

Correct answer : (4)

194.

Simplify $\frac{0.66\times {10}^{4}}{3.3\times {10}^{-4}}$ and write the result in scientific notation.

a. | 0.2 × 10 ^{7} | ||

b. | 2.0 × 10 ^{4} | ||

c. | 2.0 × 10 ^{8} | ||

d. | 2.0 × 10 ^{7} |

[Write as a product.]

= 0.2 × (10

[Use quotient of powers property.]

= (2.0 × 10

[Write 0.2 in scientific notation.]

= 2.0 × 10

[Use product of powers property.]

Correct answer : (4)

195.

Simplify $\frac{2.0\times {10}^{-9}}{6\times {10}^{-4}}$ and write the result in scientific notation.

a. | 3.3 × 10 ^{6} | ||

b. | 3.3 × 10 ^{- 6} | ||

c. | - 3.3 × 10 ^{6} | ||

d. | - 3.3 × 10 ^{- 6} |

[Write as a product.]

= 0.33 × 10

[Use quotient of powers property.]

= (3.3 × 10

[Write 0.33 in scientific notation.]

= 3.3 × 10

[Use product of powers property.]

Correct answer : (2)

196.

The mean distance of the Earth from the Moon is about 384,400 km. Write the distance in scientific notation.

a. | 1.922 × 10 ^{5} km | ||

b. | 3.844 × 10 ^{5} km | ||

c. | 3844 km | ||

d. | 0.3844 × 10 ^{5} km |

The first factor in the scientific notation of 384,400 is 3.844.

[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 5 places to the left. Use this number as the exponent of 10.]

The mean distance of the Earth from the Moon in scientific notation is about 3.844 × 10

Correct answer : (2)

197.

The total men in the Civilian Labor Force in the U.S in the year 2001 was about 7.5743 × 10^{7}. Write the number in decimal form.

a. | 7,574,300 | ||

b. | 757,430 | ||

c. | 75,743,000 | ||

d. | 757,430,000 |

[Multiplying by 10,000,000, moves the decimal point 7 places to the right.]

The total men in the Civilian Labor Force in decimal form is 75,743,000.

Correct answer : (3)

198.

Multiply 7 × 10^{7} and 5 × 10^{- 2}. Express the result in scientific notation.

a. | 3.5 × 10 ^{6} | ||

b. | 3.5 | ||

c. | 35 | ||

d. | 3.5 × 10 ^{5} |

(7 × 10

[Use commutative property of multiplication.]

= 35 × 10

[Multiply 7 and 5.]

= 35 × 10

[Add exponents.]

= 3.5 × 10

[Write 35 = 3.5 × 10

= 3.5 × 10

[Add exponents.]

Correct answer : (1)

199.

Express 760,000,000,000 in scientific notation.

a. | 7.6 × 10 ^{9} | ||

b. | 7.6 × 10 ^{8} | ||

c. | 7.6 × 10 ^{11} | ||

d. | 7.6 × 10 ^{10} |

[Move the decimal point 11 places to the left, to get a factor greater than or equal to 1 and less than 10.]

= 7.6 × 100,000,000,000

= 7.6 × 10

[The exponent of 10 is 11.]

The scientific notation of the number 760,000,000,000 is 7.6 × 10

Correct answer : (3)