General, Organic, and Biological Chemistry Fourth Edition Karen Timberlake 1.4 Scientific Notation Chapter 1 Chemistry and Measurements © 2013 Pearson Education, Inc. Lectures

© 2013 Pearson Education, Inc. Chapter 1, Section 4 2 Scientific Notation  is used to write very large or very small numbers.  is used to give the width of a human hair ( m) as 8 x m.  for a large number such as hairs is written as 1 x 10 5 hairs.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 3 Writing Numbers in Scientific Notation  A number in scientific notation contains a coefficient between 1 and 10 and a power of 10 and a unit.  For numbers larger than 1, the power of 10 is positive.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 4 Writing Numbers in Scientific Notation For numbers smaller than 1, the power of 10 is negative.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 5 Some Powers of Ten

© 2013 Pearson Education, Inc. Chapter 1, Section 4 6 Scientific Notation and Calculators  You can enter a number in scientific notation on many calculators using the EE or EXP key.  Use the (+/−) key to change the value of the exponent from positive to negative.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 7 Scientific Notation and Calculators When a calculator display appears in scientific notation, it is shown as a number between 1 and 10 followed by a space and the power of 10.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 8 Scientific Notation and Calculators T o write this number in correct scientific notation, write the coefficient and use the power of 10 as an exponent.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 9 Converting Scientific Notation to a Standard Number When a number in scientific notation has a positive power of 10,  move the decimal point to the right for the same number of places as the power of 10 and  add placeholder zeros to give the additional decimal places needed.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 10 Converting Scientific Notation to a Standard Number When a number in scientific notation has a negative power of 10,  move the decimal point to the left for the same number of places as the power of 10 and  add placeholder zeros in front of the coefficient as needed.

© 2013 Pearson Education, Inc. Chapter 1, Section 4 11 Learning Check Select the correct scientific notation for each m A. 8 x 10 8 m B. 8 x 10 −8 m C. 0.8 x 10 −7 m L A. 7.2 x 10 4 L B. 72 x 10 3 L C. 7.2 x 10 −4 L

© 2013 Pearson Education, Inc. Chapter 1, Section 4 12 Solution Select the correct scientific notation for each m B. 8 x 10 −8 m L A. 7.2 x 10 4 L

© 2013 Pearson Education, Inc. Chapter 1, Section 4 13 Learning Check Write each as a standard number x 10 −2 s A. 200 sB s C s x 10 5 g A gB gC g

© 2013 Pearson Education, Inc. Chapter 1, Section 4 14 Solution Write each as a standard number x 10 −2 s C s x 10 5 g A g