1. 1.7 Large & Small Numbers Chapter 1 Matter, Measurements, & Calculations Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings 10  m = 1x10 -6 m

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 8 x 10 -6 m. of a large number such as 4 500 000 s is written 4.5 x 10 6 s. Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

3. Writing Numbers in 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. Some Powers of Ten

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 pox virus 0.000 03 cm 3 x 10 -5 cm

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. 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. 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. 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

10. Measured Numbers A measuring tool is used to determine a quantity such as height or the mass of an object. provides numbers for a measurement called measured numbers. Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

11. . l 2.... l.... l 3.... l.... l 4.. cm The markings on the meter stick at the end of the orange line are read as the first digit 2 plus the second digit 2.7 The last digit is obtained by estimating. The end of the line might be estimated between 2.7– 2.8 as half-way (0.5) or a little more (0.6), which gives a reported length of 2.75 cm or 2.76 cm. Reading a Meter Stick

12. Known & Estimated Digits In the length reported as 2.76 cm, The digits 2 and 7 are certain (known). The final digit 6 was estimated (uncertain). All three digits (2.76) are significant including the estimated digit.

13. . l 8.... l.... l 9.... l.... l 10.. cm What is the length of the orange line? 1) 9.0 cm 2) 9.03 cm 3) 9.04 cm Learning Check

14. . l 8.... l.... l 9.... l.... l 10.. cm The length of the orange line could be reported as 2) 9.03 cm or 3) 9.04 cm The estimated digit may be slightly different. Both readings are acceptable. Solution

15. . l 3.... l.... l 4.... l.... l 5.. cm For this measurement, the first and second known digits are 4.5. Because the line ends on a mark, the estimated digit in the hundredths place is 0. This measurement is reported as 4.50 cm. Zero as a Measured Number