Scientific Notation Worksheets

**Page 14**

131.

A hydrogen atom has a mass of 1.67 × 10^{-27} kilogram. Express the mass of 4 × 10^{2} hydrogen atoms in scientific notation.

a. | 6.68 x 10 ^{-25} kilogram | ||

b. | 6.68 x 10 ^{29} kilogram | ||

c. | 6.68 x 10 ^{-29} kilogram | ||

d. | 6.68 x 10 ^{25} kilogram |

The mass of 4 x 10

= (1.67 x 4) x (10

[Use commutative property of multiplication.]

= 6.68 x (10

[Multiply 1.67 and 4.]

= 6.68 x 10

[Add the exponents.]

Correct answer : (1)

132.

The weight of an elephant is 1600 kgs. Write the number in scientific notation.

a. | 1.6 x 10 ^{3} | ||

b. | 16 x 10 ^{-3} | ||

c. | 1.6 | ||

d. | 1.6 x 10 ^{4} |

The first factor is 1.6.

[Move the decimal point such that the number is greater than 1 but less than 10.]

The second factor is 10

[As the decimal is moved 3 places to the left, take the exponent of 10 as 3.]

So, the number 1600 in scientific notation is 1.6 x 10

Correct answer : (1)

133.

Order the numbers 130 × 10^{2}, 16.3 × 10^{5}, 0.061 × 10^{4} from the greatest to the least.

a. | 130 x 10 ^{2} > 16.3 x 10^{5} > 0.061 x 10^{4} | ||

b. | 0.061 x 10 ^{4} > 16.3 x 10^{5} > 130 x 10^{2} | ||

c. | 16.3 x 10 ^{5} > 130 x 10^{2} > 0.061 x 10^{4} | ||

d. | None of the above |

[Write 130 as 1.30 x 10

= 1.30 x 10

[Add the exponents.]

= 13000

[Simplify.]

16.3 x 10

[Write 16.3 as 1.63 x 10

= 1.63 x 10

[Add the exponents.]

= 1630000

[Simplify.]

0.061 x 10

[Write 0.061 as 6.100 x 10

= 6.100 x 10

[Add the exponents.]

= 610

[Simplify.]

Since 1630000 > 13000 > 610, the order is 16.3 x 10

Correct answer : (3)

134.

In _______ notation, we change expressions from scientific notation by simplifying the product of two factors.

a. | Exponential | ||

b. | Standard | ||

c. | Scientific | ||

d. | Algebric |

Correct answer : (2)

135.

Multiply 5 × 10^{6} and 6 × 10^{-3}. Express the result in scientific notation.

a. | 3 | ||

b. | 3 x 10 ^{3} | ||

c. | 3 x 10 ^{4} | ||

d. | 30 |

(5 x 10

[Use commutative property of multiplication.]

= 30 x 10

[Multiply 5 and 6.]

= 30 x 10

[Add exponents.]

= 3 x 10

[Write 30 = 3 x 10

= 3 x 10

[Add exponents.]

Correct answer : (3)

136.

Find the values of $a$ and $b$ in the table.

3 x 10^{1} | 3 x 10 | 30 |

3 x 10^{0} | 3 x 1 | 3 |

3 x 10^{-2} | 3 x $a$ | $b$ |

a. | 0.01, 0.03 | ||

b. | 1.00, 3.00 | ||

c. | 0.10, 0.30 | ||

d. | None of the above |

[Write as a positive exponent.]

= 3 x

= 0.03

The value of

Correct answer : (1)

137.

Find the values of $a$ and $b$ in the table.

2 x 10^{2} | 2 x 100 | 200 |

2 x 10^{0} | 2 x $a$ | $b$ |

a. | $a$ = 2, $b$ = 1 | ||

b. | $a$ = 1, $b$ = 2 | ||

c. | $a$ = 1, $b$ = 3 | ||

d. | $a$ = 2, $b$ = 3 |

The value of

Correct answer : (2)

138.

Write 29000 in scientific notation.

a. | 2.9 × 10 ^{5} | ||

b. | 2.9 × 10 ^{3} | ||

c. | 2.9 × 10 ^{4} | ||

d. | None of the above |

The first factor in the scientific notation of 29000 is 2.9.

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

So, the scientific notation of 29000 is 2.9 × 10

Correct answer : (3)

139.

Write 310000000 in scientific notation.

a. | 3.1 × 10 ^{8} | ||

b. | 3.1 × 10 ^{9} | ||

c. | 3.1 × 10 ^{7} | ||

d. | 3.1 × 10 ^{6} |

The first factor in the scientific notation of 310000000 is 3.1.

[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 310000000 is 3.1 × 10

Correct answer : (1)

140.

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 x 10 ^{1} | ||

b. | 3.31 x 10 ^{3} | ||

c. | 3.31 x 10 ^{2} | ||

d. | None of the above |

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 x 10

Correct answer : (3)