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4.3 An Application of Exponents: Scientific Notation

4.3 An Application of Exponents: Scientific Notation. Objective 1 . Express numbers in scientific notation. Slide 4.3-3. Express numbers in scientific notation.

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4.3 An Application of Exponents: Scientific Notation

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  1. 4.3 An Application of Exponents: Scientific Notation

  2. Objective 1 Express numbers in scientific notation. Slide 4.3-3

  3. Express numbers in scientific notation. 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. 0.0000006 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. 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 × 104, since Slide 4.3-4

  4. Express numbers in scientific notation. Writing a Number in Scientific Notation Step 1:Move the decimal point to the right of the first nonzero digit. Step 2:Count the number of places you moved the decimal point. Step 3:The number of places inStep 2is the absolute value of the exponent on 10. Step 4:The exponent on 10 is positive if the original number is greater than the number inStep 1.The exponent is negative if the original number is less than inStep 1. If the decimal point is not moved, the exponent is 0. Slide 4.3-5

  5. CLASSROOM EXAMPLE 1 Using Scientific Notation Write each in scientific notation. Solution: The exponent is positiveif the original number is extremely “large”. Likewise, the exponent will be negative if the original if the original number is extremely “small”. Slide 4.3-6

  6. Objective 2 Convert numbers in scientific notation to numbers without exponents. Slide 4.3-7

  7. Convert numbers in scientific notation to numbers without exponents. 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. Slide 4.3-8

  8. CLASSROOM EXAMPLE 2 Writing Numbers without Exponents Write each number without exponents. Solution: Slide 4.3-9

  9. Objective 3 Use scientific notation in calculators. Slide 4.3-10

  10. CLASSROOM EXAMPLE 3 Multiplying and Dividing with Scientific Notation Perform each calculation. Write answers in scientific notation and also without exponents. Solution: Multiplying or dividing numbers written in scientific notation may produce an answer in the form a ×100. Since 100= 1, a ×100= a. For example, Also, if a =1, then a ×10n= 10n.For example, we could write 1,000,000 as 106instead of 1 × 106. Slide 4.3-11

  11. CLASSROOM EXAMPLE 4 Using Scientific Notation to Solve an Application The speed of light is approximately 3.0 × 105 km per sec. How far does light travel in 6.0 × 101 sec? (Source: World Almanac and Book of Facts.) Solution: Light would travel 18,000,000 km in 6 seconds. Slide 4.3-12

  12. CLASSROOM EXAMPLE 5 Using Scientific Notation to Solve an Application The speed of light is approximately 3.0 × 105 km per sec. How many seconds does it take light to travel approximately 1.5 × 108 km from the sun to Earth? (Source: World Almanac and Book of Facts.) Solution: It takes 500 seconds for light from the sun to reach Earth. Slide 4.3-13

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