4.3 Scientific Notation

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.

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 cm = 2.5 x cm

Scientific Notation  Scientific Notation: a x 10 b where 1 ≤ a < 10 and b is integer  E.g x x x 10 22

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

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

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 in Standard Notation 2.1 x = 2.1 x 1/10,000 = (Move the decimal point 4 places to the left)

Your Turn Write the following in standard notation x 10 6  2,370, x  x 10 0  9.77

Simplifying Calculation

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

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

Speed of Light  ( km) / = 5 x 10 2 x 10 3 / (3 x ) = (5/3)( (-9) ) = (5/3)10 sec