The document discusses scientific notation, which is used to write very large or very small numbers in a standardized way. Scientific notation represents a number as a coefficient multiplied by a power of 10. The power of 10 indicates how many places the decimal point is moved. Examples are provided to demonstrate how numbers are converted between standard and scientific notation formats. Practice problems are included for the reader to test their understanding of converting between the two number representation systems.

1. Chapter 2 Measurements 2.2 Scientific Notation Basic Chemistry Copyright © 2011 Pearson Education, Inc.

2. Scientific Notation Scientific notation is used to write very large or very small numbers for the width of a human hair (0.000 008 m) is written as 8 x 10 -6 m for a large number such as 4 500 000 s is written as 4.5 x 10 6 s Basic Chemistry Copyright © 2011 Pearson Education, Inc.

3. Scientific Notation A number written in scientific notation contains a coefficient and a power of 10. c oefficient power of ten coefficient power of ten 1.5 x 10 2 7.35 x 10 -4 To write a number in scientific notation, the decimal point is moved after the first digit. The spaces moved are shown as a power of ten. 52 000 . = 5.2 x 10 4 0 . 003 78 = 3.78 x 10 -3 4 spaces left 3 spaces right Basic Chemistry Copyright © 2011 Pearson Education, Inc.

4. Some Powers of Ten Basic Chemistry Copyright © 2011 Pearson Education, Inc.

5. Comparing Numbers in Standard and Scientific Notation Here are some numbers written in standard format and in scientific notation. Number in Standard Format Scientific Notation Diameter of the Earth 12 800 000 m 1.28 x 10 7 m Mass of a human 68 kg 6.8 x 10 1 kg Length of a virus 0.000 03 cm 3 x 10 -5 cm Basic Chemistry Copyright © 2011 Pearson Education, Inc.

6. Learning Check Select the correct scientific notation for each. A. 0.000 008 1) 8 x 10 6 2) 8 x 10 -6 3) 0.8 x 10 -5 B. 72 000 1) 7.2 x 10 4 2) 72 x 10 3 3) 7.2 x 10 -4 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

7. Solution Select the correct scientific notation for each. A. 0.000 008 2) 8 x 10 -6 B. 72 000 1) 7.2 x 10 4 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

8. Learning Check Write each as a standard number. A. 2.0 x 10 -2 1) 200 2) 0.0020 3) 0.020 B. 1.8 x 10 5 1) 180 000 2) 0.000 018 3) 18 000 Basic Chemistry Copyright © 2011 Pearson Education, Inc.

9. Solution Write each as a standard number. A. 2.0 x 10 -2 3) 0.020 B. 1.8 x 10 5 1) 180 000 Basic Chemistry Copyright © 2011 Pearson Education, Inc.