Chapter 5 Section 3

Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. An Application of Exponents: Scientific Notation Express numbers in scientific notation. Convert numbers in scientific notation to numbers without exponents. Use scientific notation in calculations

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Express numbers in scientific notation. Slide 5.3-3

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Numbers occurring in science are often extremely large (as the distance from Earth to sun, 93,000,000 mi) or extremely small (wavelength of yellow-green light, approx m). Due to the difficulty of working with many zeros, scientists often express such numbers with exponents, using a form called scientific notation. Scientific Notation A number is written in scientific notation when it is expressed in the form where 1 ≤ |a| < 10 and n is an integer. Express numbers in scientific notation. A number in scientific notation is always written with the decimal point after the first nonzero digit an then multiplied by the appropriate power of 10. For example 56,200 is written 5.62 × 10 4, since Slide 5.3-4

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Writing a Number in Scientific Notation Step 3: The number of places in Step 2 is the absolute value of the exponent on 10. Step 2: Count the number of places you moved the decimal point. Step 1: Move the decimal point to the right of the first nonzero digit. Step 4: The exponent on 10 is positive if the original number is greater than the number in Step 1. The exponent is negative if the original number is less than in Step 1. If the decimal point is not moved, the exponent is 0. Slide 5.3-5

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Write each in scientific notation. The exponent is positive if the original number is extremely “large”. Likewise, the exponent will be negative if the original if the original number is extremely “small”. Slide EXAMPLE 1 Using Scientific Notation

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Convert numbers in scientific notation to numbers without exponents. Slide 5.3-7

Copyright © 2012, 2008, 2004 Pearson Education, Inc. To convert a number written scientific notation to a number without exponents, work in reverse. Multiplying a number by a positive power of 10 will make the number greater. Multiplying by a negative power of 10 will make the number less. Convert numbers in scientific notation to numbers without exponents. Slide 5.3-8

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Write each number without exponents. Slide EXAMPLE 2 Writing Numbers without Exponents

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 3 Use scientific notation in calculators. Slide

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Perform each calculation. Write answers in scientific notation and also without exponents. Multiplying or dividing numbers written in scientific notation may produce an answer in the form a × Since 10 0 = 1, a × 10 0 = a. For example, Also, if a =1, then a × 10 n = 10 n. For example, we could write 1,000,000 as 10 6 instead of 1 × Slide EXAMPLE 3 Multiplying and Dividing with Scientific Notation

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Light would travel 18,000,000 km in 6 seconds. The speed of light is approximately 3.0 × 10 5 km per sec. How far does light travel in 6.0 × 10 1 sec? (Source: World Almanac and Book of Facts.) Slide EXAMPLE 4 Using Scientific Notation to Solve an Application

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: The speed of light is approximately 3.0 × 10 5 km per sec. How many seconds does it take light to travel approximately 1.5 × 10 8 km from the sun to Earth? (Source: World Almanac and Book of Facts.) It takes 500 seconds for light from the sun to reach Earth. Slide EXAMPLE 5 Using Scientific Notation to Solve an Application