Scientific Notation Worksheets

**Page 13**

121.

Identify 5.849 × 10^{6} in standard form.

a. | 5849 | ||

b. | 584900 | ||

c. | 58490 | ||

d. | 5849000 |

5.849 × 10

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

Correct answer : (4)

122.

Write 5.4 × 10^{-5} in standard form.

a. | 0.00054 | ||

b. | 0.000054 | ||

c. | 0.0054 | ||

d. | 54000.0 |

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

So, the standard form of 5.4 x 10

Correct answer : (2)

123.

Express 80000000 in scientific notation.

a. | 8 × 10 ^{8} | ||

b. | 8 × 10 ^{7} | ||

c. | 8 | ||

d. | 8 × 10 ^{6} |

The first factor is 8.

[Move the decimal point 7 places to the left to get a number between 0 and 10.]

The second factor is 10

[As the decimal is moved 7 places to the right, take 7 as exponent of 10.]

So, 80000000 can be written in scientific notation as 8 × 10

Correct answer : (2)

124.

Solve the expression (7.3 × 10^{3}) (4.3 × 10^{4}) and express the result in scientific notation.

a. | 3.139 x 10 ^{6} | ||

b. | 3.139 | ||

c. | 3.139 x 10 ^{7} | ||

d. | 3.139 x 10 ^{8} |

[Use multiplication properties.]

= 31.39 x 10

[Use product of powers property.]

= (3.139 x 10

[Write 31.39 in scientific notation.]

= 3.139 x 10

[Use product of powers property.]

Correct answer : (4)

125.

Solve (5.9 × 10^{7}) (6.5 × 10^{-5}) and write the result in scientific notation.

a. | 3.835 | ||

b. | 3.835 x 10 ^{3} | ||

c. | 3.835 x 10 ^{-3} | ||

d. | 3.835 x 10 ^{2} |

[Use multiplication properties.]

= (38.35) (10

[Use product of powers property.]

= (3.835 x 10

[Write 38.35 in scientific notation.]

= 3.835 x 10

[Use product of powers property.]

Correct answer : (2)

126.

Simplify (0.34 × 10^{4}) / (3.4 × 10^{-4}) and write the result in scientific notation.

a. | 1.0 x 10 ^{8} | ||

b. | 1.0 x 10 ^{-7} | ||

c. | -1.0 x 10 ^{7} | ||

d. | 1.0 x 10 ^{7} |

[Write as a product.]

= 0.1 x (10

[Use quotient of powers property.]

= (1.0 x 10

[Write 0.1 in scientific notation.]

= 1.0 x 10

[Use product of powers property.]

Correct answer : (4)

127.

Simplify (2.0 × 10^{-13}) / (10 × 10^{-9}) and write the result in scientific notation.

a. | 2 x 10 ^{5} | ||

b. | -2 x 10 ^{5} | ||

c. | 2 x 10 ^{-5} | ||

d. | -2 x 10 ^{-5} |

[Write as a product.]

= 0.2 x 10

[Use quotient of powers property.]

= (2 x 10

[Write 0.2 in scientific notation.]

= 2 x 10

[Use product of powers property.]

Correct answer : (3)

128.

Simplify:

(7 × 10^{-7})^{2}

a. | 4.9 × 10 ^{13} | ||

b. | - 4.9 × 10 ^{13} | ||

c. | 4.9 × 10 ^{- 13} | ||

d. | - 4.9 × 10 ^{- 13} |

[Use power of a product property.]

= 49 × 10

[Use power of a power property.]

= (4.9 × 10

[Write 49 in scientific notation.]

= 4.9 × 10

[Use product of powers property.]

Correct answer : (3)

129.

Write 83972 in scientific notation.

a. | 839.72 x 10 ^{16} | ||

b. | 83.972 x 10 ^{4} | ||

c. | 83.972 | ||

d. | 8.3972 x 10 ^{4} |

The first factor is 8.3972.

[Move the decimal point such that the number is between 1 and 10.]

The second factor is 10

[As the decimal is moved 4 places to the left, take the exponent of 10 as 4.]

So, the number 83972 in scientific notation is 8.3972 x 10

Correct answer : (4)

130.

A teacher asked four students to evaluate 5 × 10^{4} . Sunny answered 5000, Jeff answered 50000, Andy answered 500000, and William answered 5000000. Who among the four was correct?

a. | Andy | ||

b. | William | ||

c. | Jeff | ||

d. | Sunny |

[Evaluate power.]

= 50000

[Multiply 5 and 10000.]

So, Jeff is correct.

Correct answer : (3)