3 1.2 Expressing Numbers

Practice questions

  1. Express these numbers in scientific notation.
      1. [latex]{56.9}[/latex]
      2. [latex]{563,000}[/latex]
      3. [latex]{0.0804}[/latex]
      4. [latex]{0.00000667}[/latex]
  2. Express these numbers in scientific notation.
      1. [latex]{0.00656}[/latex]
      2. [latex]{65,600}[/latex]
      3. [latex]{4567,000}[/latex]
      4. [latex]{0.000005507}[/latex]
  3. Express these numbers in standard notation.
      1. [latex]{1.381{\times}10^{5}}[/latex]
      2. [latex]{5.22{\times}10^{-7}}[/latex]
      3. [latex]{9.998{\times}10^{4}}[/latex]
      4. [latex]{8.09{\times}10^{0}}[/latex]
      5. [latex]{3.088{\times}10^{-5}}[/latex]
  4. These numbers are not written in proper scientific notation. Rewrite them so that they are in proper scientific notation.
      1. [latex]{72.44{\times}10^{3}}[/latex]
      2. [latex]{9,943{\times}10^{-5}}[/latex]
      3. [latex]{588,399{\times}10^{2}}[/latex]
      4. [latex]{0.234{\times}10^{-3}}[/latex]
  5. How many significant figures do these numbers have?
      1. [latex]{23}[/latex]
      2. [latex]{23.0}[/latex]
      3. [latex]{0.00023}[/latex]
      4. [latex]{0.0002302}[/latex]
      5. [latex]{1.2000{\times}10^{5}}[/latex]
  6. Compute and express each answer with the proper number of significant figures, rounding as necessary.
      1. [latex]{56.0 + 3.44 =?}[/latex]
      2. [latex]{0.00665 + 1.004 =?}[/latex]
      3. [latex]{45.99 - 32.8 =?}[/latex]
      4. [latex]{45.99 - 32.8 + 75.02 =?}[/latex]
  7. Compute and express each answer with the proper number of significant figures, rounding as necessary.
      1. [latex]{56.7{\times}66.99 =?}[/latex]
      2. [latex]{{\frac{1000}{77}} =?}[/latex]
      3. [latex]{{\frac{1000}{77.0}} =?}[/latex]
      4. [latex]{6.022{\times}1.89 =?}[/latex]

 Solutions

  1. Scientific notations are as below.
    1. [latex]{5.69{\times}10^{1}}[/latex]
    2. [latex]{5.631{\times}10^{5}}[/latex]
    3. [latex]{8.04{\times}10^{-2}}[/latex]
    4. [latex]{6.67{\times}10^{-6}}[/latex]
  2. Scientific notations are as below.
    1. [latex]{6.56{\times}10^{-3}}[/latex]
    2. [latex]{6.56{\times}10^{4}}[/latex]
    3. [latex]{4.567{\times}10^{6}}[/latex]
    4. [latex]{5.507{\times}10^{-6}}[/latex]
  3. The answers are as follows.
    1. [latex]{138,100}[/latex]
    2. [latex]{0.000000522}[/latex]
    3. [latex]{99,980}[/latex]
    4. [latex]{8.08}[/latex]
    5. [latex]{0.00003088}[/latex]
  4. The answers are as follows.
    1. [latex]{7.244{\times}10^{4}}[/latex]
    2. [latex]{9.943{\times}10^{-2}}[/latex]
    3. [latex]{5.88399{\times}10^{7}}[/latex]
    4. [latex]{2.34{\times}10^{-4}}[/latex]
  5. The answers are as follows.
    1. 2
    2. 3
    3. 2
    4. 4
    5. 5
  6. The answers are as follows.
    1. [latex]{59.4}[/latex]
    2. [latex]{1.011}[/latex]
    3. [latex]{13.2}[/latex]
    4. [latex]{88.2}[/latex]
  7. The answers are as follows.
    1. [latex]{3.80{\times}{10}^{3}}[/latex]
    2. [latex]{0.013}[/latex]
    3. [latex]{0.0130}[/latex]
    4. [latex]{11.4}[/latex]

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