1. 1 Chapter 2 Measurements 2.2 Scientific Notation Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

2. 2 Scientific Notation 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 as: 8 x 10 -6 m Of a large number such as 2 500 000 s is written as: 2.5 x 10 6 s Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

3. 3 2.2 Scientific Notation A number in scientific notation contains a coefficient and a power of 10. coefficient 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 0.00378 = 3.78 x 10 -3 4 spaces left 3 spaces right

4. 4 Some Powers of Ten

5. 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 Earth 12 800 000 m1.28 x 10 7 m Mass of a human 68 kg 6.8 x 10 1 kg Length of a pox virus 0.000 03 cm3 x 10 -5 cm

6. 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

7. 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

8. 8 Learning Check Write each as a standard number. A. 2.0 x 10 -2 1) 2002) 0.00203) 0.020 B. 1.8 x 10 5 1) 180 0002) 0.000 0183) 18 000

9. 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