chapter 5 section 3. objectives 1 copyright © 2012, 2008, 2004 pearson education, inc. an...

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.

5.3

2

3


Objective 1


Slide 5.3-3


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 NotationA number is written in scientific notation when it is expressed in the form

where 1 ≤ |a| < 10 and n is an integer.


10 ,na

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 410,00056,200 5.62 5 .1.62 0

Slide 5.3-4


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


Solution:

Write each in scientific notation.

0.0571 25.71 10

92.14 10

56.2 10

2,140,000,000

0.000062

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 5.3-6

EXAMPLE 1 Using Scientific Notation


Objective 2


Slide 5.3-7


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 5.3-8


Solution:

870,000

0.00000328

Write each number without exponents.

58.7 10

63.28 10

Slide 5.3-9

EXAMPLE 2 Writing Numbers without Exponents


Objective 3

Use scientific notation in calculators.

Slide 5.3-10


Solution:

401.5 1

302 1

5 23 10 5 10 2

5

4.8 10

2.4 10

3015 1 15,000

0.002

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 × 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 106 instead of 1 × 106.

4 4 010 108 5 40 0 40.1

Slide 5.3-11

EXAMPLE 3 Multiplying and Dividing with Scientific Notation


Solution:

5 1103 0 1. 06.0d

d rt

Light would travel 18,000,000 km in 6 seconds.

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.)

61018d 71.8 or 18,000,001 00 d km

Slide 5.3-12

EXAMPLE 4 Using Scientific Notation to Solve an Application


Solution:

rt

d

30.5 10t

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.)

8

5

101 5

1

.

03.0t

25 or 5010 0 sect

It takes 500 seconds for light from the sun to reach Earth.

Slide 5.3-13

EXAMPLE 5 Using Scientific Notation to Solve an Application

chapter 5 section 3. objectives 1 copyright © 2012, 2008, 2004 pearson education, inc. an...

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