2 2 scientific_notation

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2 2 scientific_notation

  1. 1. Chapter 2 Measurements <ul><li>2.2 </li></ul><ul><li>Scientific Notation </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  2. 2. Scientific Notation <ul><li>Scientific notation </li></ul><ul><li>is used to write very large or very small numbers </li></ul><ul><li>for the width of a human hair (0.000 008 m) is written as </li></ul><ul><li>8 x 10 -6 m </li></ul><ul><li>for a large number such as 4 500 000 s is written as </li></ul><ul><li>4.5 x 10 6 s </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  3. 3. Scientific Notation <ul><li>A number written in scientific notation contains a coefficient and a power of 10. </li></ul><ul><li>c oefficient power of ten coefficient power of ten </li></ul><ul><li> 1.5 x 10 2 7.35 x 10 -4 </li></ul><ul><li>To write a number in scientific notation, the decimal point is moved after the first digit. </li></ul><ul><li>The spaces moved are shown as a power of ten. </li></ul><ul><li>52 000 . = 5.2 x 10 4 0 . 003 78 = 3.78 x 10 -3 </li></ul><ul><li> </li></ul><ul><li>4 spaces left 3 spaces right </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  4. 4. Some Powers of Ten Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  5. 5. Comparing Numbers in Standard and Scientific Notation <ul><li>Here are some numbers written in standard format </li></ul><ul><li>and in scientific notation. </li></ul><ul><li>Number in </li></ul><ul><li>Standard Format Scientific Notation </li></ul><ul><li>Diameter of the Earth </li></ul><ul><li>12 800 000 m 1.28 x 10 7 m </li></ul><ul><li>Mass of a human </li></ul><ul><li>68 kg 6.8 x 10 1 kg </li></ul><ul><li>Length of a virus </li></ul><ul><li>0.000 03 cm 3 x 10 -5 cm </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  6. 6. Learning Check <ul><li>Select the correct scientific notation for each. </li></ul><ul><li>A. 0.000 008 </li></ul><ul><li>1) 8 x 10 6 2) 8 x 10 -6 3) 0.8 x 10 -5 </li></ul><ul><li>B. 72 000 </li></ul><ul><li>1) 7.2 x 10 4 2) 72 x 10 3 3) 7.2 x 10 -4 </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  7. 7. Solution <ul><li>Select the correct scientific notation for each. </li></ul><ul><li>A. 0.000 008 </li></ul><ul><li>2) 8 x 10 -6 </li></ul><ul><li>B. 72 000 </li></ul><ul><li>1) 7.2 x 10 4 </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  8. 8. Learning Check <ul><li>Write each as a standard number. </li></ul><ul><li>A. 2.0 x 10 -2 </li></ul><ul><li> 1) 200 2) 0.0020 3) 0.020 </li></ul><ul><li>B. 1.8 x 10 5 </li></ul><ul><li> 1) 180 000 2) 0.000 018 3) 18 000 </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  9. 9. Solution <ul><li>Write each as a standard number. </li></ul><ul><li>A. 2.0 x 10 -2 </li></ul><ul><li> 3) 0.020 </li></ul><ul><li>B. 1.8 x 10 5 </li></ul><ul><li> 1) 180 000 </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.

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