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When performing calculations with scientific notation, be sure to write the answer in proper scientific notation. For example, consider the product ( 7 × 10 4 ) ( 5 × 10 6 ) = 35 × 10 10 . The answer is not in proper scientific notation because 35 is greater than 10. Consider 35 as 3.5 × 10. That adds a ten to the exponent of the answer.

( 35 ) × 10 10 = ( 3.5 × 10 ) × 10 10 = 3.5 × ( 10 × 10 10 ) = 3.5 × 10 11

Using scientific notation

Perform the operations and write the answer in scientific notation.

  1. ( 8.14 × 10 −7 ) ( 6.5 × 10 10 )
  2. ( 4 × 10 5 ) ÷ ( −1.52 × 10 9 )
  3. ( 2.7 × 10 5 ) ( 6.04 × 10 13 )
  4. ( 1.2 × 10 8 ) ÷ ( 9.6 × 10 5 )
  5. ( 3.33 × 10 4 ) ( −1.05 × 10 7 ) ( 5.62 × 10 5 )

  1. ( 8.14 × 10 −7 ) ( 6.5 × 10 10 ) = ( 8.14 × 6.5 ) ( 10 −7 × 10 10 ) Commutative and associative properties of multiplication = ( 52.91 ) ( 10 3 ) Product rule of exponents = 5.291 × 10 4 Scientific notation

  2. ( 4 × 10 5 ) ÷ ( −1.52 × 10 9 ) = ( 4 −1.52 ) ( 10 5 10 9 ) Commutative and associative properties of multiplication ( −2.63 ) ( 10 −4 ) Quotient rule of exponents = −2.63 × 10 −4 Scientific notation

  3. ( 2.7 × 10 5 ) ( 6.04 × 10 13 ) = ( 2.7 × 6.04 ) ( 10 5 × 10 13 ) Commutative and associative properties of multiplication = ( 16.308 ) ( 10 18 ) Product rule of exponents = 1.6308 × 10 19 Scientific notation

  4. ( 1.2 × 10 8 ) ÷ ( 9.6 × 10 5 ) = ( 1.2 9.6 ) ( 10 8 10 5 ) Commutative and associative properties of multiplication = ( 0.125 ) ( 10 3 ) Quotient rule of exponents = 1.25 × 10 2 Scientific notation

  5. ( 3.33 × 10 4 ) ( −1.05 × 10 7 ) ( 5.62 × 10 5 ) = [ 3.33 × ( −1.05 ) × 5.62 ] ( 10 4 × 10 7 × 10 5 ) ( −19.65 ) ( 10 16 ) = −1.965 × 10 17

Perform the operations and write the answer in scientific notation.

  1. ( −7.5 × 10 8 ) ( 1.13 × 10 −2 )
  2. ( 1.24 × 10 11 ) ÷ ( 1.55 × 10 18 )
  3. ( 3.72 × 10 9 ) ( 8 × 10 3 )
  4. ( 9.933 × 10 23 ) ÷ ( 2.31 × 10 17 )
  5. ( −6.04 × 10 9 ) ( 7.3 × 10 2 ) ( −2.81 × 10 2 )
  1. 8.475 × 10 6
  2. 8 × 10 8
  3. 2.976 × 10 13
  4. 4.3 × 10 6
  5. 1.24 × 10 15

Applying scientific notation to solve problems

In April 2014, the population of the United States was about 308,000,000 people. The national debt was about $17,547,000,000,000. Write each number in scientific notation, rounding figures to two decimal places, and find the amount of the debt per U.S. citizen. Write the answer in both scientific and standard notations.

The population was 308,000,000 = 3.08 × 10 8 .

The national debt was $ 17,547,000,000,000 $ 1.75 × 10 13 .

To find the amount of debt per citizen, divide the national debt by the number of citizens.

( 1.75 × 10 13 ) ÷ ( 3.08 × 10 8 ) = ( 1.75 3.08 ) ( 10 13 10 8 ) 0.57 × 10 5 = 5.7 × 10 4

The debt per citizen at the time was about $ 5.7 × 10 4 , or $57,000.

An average human body contains around 30,000,000,000,000 red blood cells. Each cell measures approximately 0.000008 m long. Write each number in scientific notation and find the total length if the cells were laid end-to-end. Write the answer in both scientific and standard notations.

Number of cells: 3 × 10 13 ; length of a cell: 8 × 10 −6 m; total length: 2.4 × 10 8 m or 240 , 000 , 000 m.

Access these online resources for additional instruction and practice with exponents and scientific notation.

Practice Key Terms 1

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Source:  OpenStax, Selected topics in algebra. OpenStax CNX. Sep 02, 2015 Download for free at http://legacy.cnx.org/content/col11877/1.2
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