1. 4.3 Scientific Notation

2. Objectives 1.Convert a number from standard notation to scientific notation. 2.Convert a number from scientific notation to standard notation. 3.Use scientific notation to simplify an expression.

3. Scientific Notation  Why use S.N.? To express very large or very small numbers in a compact mannter  E.g., Distance between Earth and Sun 150,000,000 km = 1.5 x 10 8 km Wavelength of UV from mercury arc 0.000025 cm = 2.5 x 10 -5 cm

4. Scientific Notation  Scientific Notation: a x 10 b where 1 ≤ a < 10 and b is integer  E.g. 3.67 x 10 6 2.24 x 10 -4 9.875 x 10 22

5. Example  Convert the following to S.N. to the indicated significant figures. 1.World population (2) 7,198,000,000  7.2 x 10 9 2.DNA molecule (2) 0.0000000025 m (8 zeros)  2.5 x 10 -9 m 3.Human hair (2) 0.00002 m to 0.00018 m  2.0 x 10 -5 m to 1.8 x 10 -4 m

6. Convert S.N to Standard Notation  A positive exponent indicates a large number  A negative exponent indicates a small number  For example 9.3 x 10 7 is a large number. Move decimal point 7 places to the right. 9.3 x 10 7 = 9.3 x 10,000,000 = 93,000,000

7. Example 1.Write 3.4 x 10 5 in Standard Notation 3.4 x 10 5 = 3.4 x 100,000 = 340,000 (Move decimal point 5 places to the right) 2.Write 2.1 x 10 -4 in Standard Notation 2.1 x 10 -4 = 2.1 x 1/10,000 = 0.00021 (Move the decimal point 4 places to the left)

8. Your Turn Write the following in standard notation. 1.2.37 x 10 6  2,370,000 2.8.375 x 10 -3  0.008375 3.9.77 x 10 0  9.77

9. Simplifying Calculation

10. Simplifying Calculations E = mc 2 c = 3.0 x 10 8 m/sec Let m = 1 g = 10 -3 kg E = 10 -3 x (3.0 x 10 8 ) 2 = 9.0 x 10 -3 x 10 16 = 9.0 x 10 16 joules (100 watt bulb uses 100 joules every hour.)

11. Speed of Light  In vacuum, light travels 1 meter in 0.000000003 sec. How long does it take for light travel 500 km (312 mi)?  Solution t 1 /d 1 = t 2 /d 2 0.000000003/1 = t 2 /(500 10 3 ) 3.0 x 10 -9 /1 = t 2 /(5 x 10 2 x 10 3 ) (3.0 x 10 -9 )(5 x 10 2 x 10 3 ) = t 2 = (3 x 5)(10 -9+2+3 ) = 15 x 10 -4 = 1.5 x 10 -3 sec

12. Speed of Light  (500 10 3 km) / 0.000000003 = 5 x 10 2 x 10 3 / (3 x 10 -9 ) = (5/3)(10 2+3-(-9) ) = (5/3)10 sec