1. Measurements 1.2 Scientific Notation Copyright © 2009 by Pearson Education, Inc.

2. 2 Scientific Notation is used to write very large or very small numbers. for the width of a human hair of 0.000 008 m is written 8 x 10 -6 m. of a large number such as 4 500 000 s is written 4.5 x 10 6 s. Copyright © 2009 by Pearson Education, Inc.

3. 3 Numbers in Scientific Notation A number written in scientific notation contains a coefficient. power of 10. Examples: coefficient power of ten coefficient power of ten 1.5 x 10 2 7.35 x 10 -4

4. 4 Writing Numbers in Scientific Notation To write a number in scientific notation, move the decimal point to give a number 1-9. show the spaces moved as a power of 10. Examples: 52 000. = 5.2 x 10 4 0.00178 = 1.78 x 10 -3 4 spaces left 3 spaces right

5. 5 Some Powers of 10

6. 6 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 typical human 68 kg 6.8 x 10 1 kg Length of a pox virus 0.000 03 cm 3 x 10 -5 cm

7. 7 Study Tip: Scientific Notation In a number 10 or larger, the decimal point is moved to the left to give a positive power of 10 In a number less than 1, the decimal point is moved to the right to give a negative power of 10

8. 8 Learning Check Select the correct scientific notation for each. A. 0.000 008 m 1) 8 x 10 6 m,2) 8 x 10 -6 m,3) 0.8 x 10 -5 m B. 72 000 g 1) 7.2 x 10 4 g, 2) 72 x 10 3 g,3) 7.2 x 10 -4 g

9. 9 Solution Select the correct scientific notation for each. A. 0.000 008 m 2) 8 x 10 -6 m B. 72 000 g 1) 7.2 x 10 4 g

10. 10 Learning Check Write each as a standard number. A. 2.0 x 10 -2 L 1) 200 L,2) 0.0020 L, 3) 0.020 L B. 1.8 x 10 5 g 1) 180 000 g, 2) 0.000 018 g, 3) 18 000 g

11. 11 Solution Write each as a standard number. A. 2.0 x 10 -2 L 3) 0.020 L B. 1.8 x 10 5 g 1) 180 000 g