Holt Algebra 1 7-2 Powers of 10 and Scientific Notation 7-2 Powers of 10 and Scientific Notation Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson.

Holt Algebra 1

7-2 Powers of 10 and Scientific Notation7-2 Powers of 10 and Scientific Notation

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

7-2 Powers of 10 and Scientific Notation

Warm UpEvaluate each expression.

1. 123 1,000

2. 123 1,000

3. 0.003 100

4. 0.003 100

5. 104

6. 10–4

7. 230

123,000

0.123

0.3

0.00003

10,000

0.0001

1

Holt Algebra 1


Evaluate and multiply by powers of 10.Convert between standard notation and scientific notation.

Objectives

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scientific notation

Vocabulary

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The table shows relationships between several powers of 10.

Each time you divide by 10, the exponent decreases by 1 and the decimal point moves one place to the left.

Holt Algebra 1


The table shows relationships between several powers of 10.

Each time you multiply by 10, the exponent increases by 1 and the decimal point moves one place to the right.

Holt Algebra 1


Holt Algebra 1


Find the value of each power of 10.

Example 1: Evaluating Powers of 10

Start with 1 and move the decimal point six places to the left.

A. 10–6 C. 109 B. 104

1,000,000,000

Start with 1 and move the decimal point four places to the right.

Start with 1 and move the decimal point nine places to the right.

10,0000.000001

Holt Algebra 1


You may need to add zeros to the right or left of a number in order to move the decimal point in that direction.

Writing Math

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Check It Out! Example 1

Find the value of each power of 10.

a. 10–2 c. 1010 b. 105

10,000,000,000100,0000.01

Start with 1 and move the decimal point two places to the left.

Start with 1 and move the decimal point five places to the right.

Start with 1 and move the decimal point ten places to the right.

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If you do not see a decimal point in a number, it is understood to be at the end of the number.

Reading Math

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Write each number as a power of 10.

Example 2: Writing Powers of 10

A. 1,000,000

The decimal point is six places to the right of 1, so the exponent is 6.

B. 0.0001 C. 1,000

The decimal point is four places to the left of 1, so the exponent is –4.

The decimal point is three places to the right of 1, so the exponent is 3.

Holt Algebra 1



Write each number as a power of 10.

a. 100,000,000 b. 0.0001 c. 0.1

The decimal point is eight places to the right of 1, so the exponent is 8.

The decimal point is four places to the left of 1, so the exponent is –4.

The decimal point is one place to the left of 1, so the exponent is –1.

Holt Algebra 1


You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1.

Multiplying by Powers of 10

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Find the value of each expression.

Example 3: Multiplying by Powers of 10

A. 23.89 108

23.8 9 0 0 0 0 0 0

2,389,000,000

Move the decimal point 8 places to the right.

B. 467 10–3

4 6 7

0.467

Move the decimal point 3 places to the left.

Holt Algebra 1




a. 853.4 105

853.4 0 0 0 0 Move the decimal point 5 places to the right.

85,340,000

b. 0.163 10–2

0.0 0163

0.00163

Move the decimal point 2 places to the left.

Holt Algebra 1


Scientific notation is a method of writing numbers that are very large or very small. A number written in scientific notation has two parts that are multiplied.

The first part is a number that is greater than or equal to 1 and less than 10.

The second part is a power of 10.

Holt Algebra 1


Example 4A: Astronomy Application

Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km.

Write Saturn’s diameter in standard form.

1 2 0 0 0 0

120,000 km

Move the decimal point 5 places to the right.

Holt Algebra 1


Write Saturn’s distance from the Sun in scientific notation.

1,427,000,000

1,4 2 7,0 0 0,0 0 0

9 places

Example 4B: Astronomy Application

Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km.

Count the number of places you need to move the decimal point to get a number between 1 and 10.

Use that number as the exponent of 10. 1.427 109 km

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Standard form refers to the usual way that numbers are written—not in scientific notation.

Reading Math

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Check It Out! Example 4a

Use the information above to write Jupiter’s diameter in scientific notation.

143,000 km

1 4 3 0 0 0

5 places

Count the number of places you need to move the decimal point to get a number between 1 and 10.

Use that number as the exponent of 10. 1.43 105 km

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Check It Out! Example 4b

Use the information above to write Jupiter’s orbital speed in standard form.

1 3 0 0 0 Move the decimal point 4 places to the right.

13,000 m/s

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Order the list of numbers from least to greatest.

Example 5: Comparing and Ordering Numbers in Scientific Notation

Step 1 List the numbers in order by powers of 10.

Step 2 Order the numbers that have the same power of 10

Holt Algebra 1


Order the list of numbers from least to greatest.


Step 1 List the numbers in order by powers of 10.

Step 2 Order the numbers that have the same power of 10

2 10-12, 4 10-3, 5.2 10-3, 3 1014, 4.5 1014, 4.5 1030

Holt Algebra 1


Example 6: Astronomy Application

Light from the Sun travels at about miles per second. It takes about 15,000 seconds for the light to reach Neptune. Find the approximate distance from the Sun to Neptune. Write your answer in scientific notation.

distance = rate time Write 15,000 in scientific notation.

Use the Commutative and Associative Properties to group.

Multiply within each group.mi

Holt Algebra 1



Light travels at about miles per second. Find the approximate distance that light travels in one hour. Write your answer in scientific notation.

distance = rate time Write 3,600 in scientific notation.

Multiply within each group.

Use the Commutative and Associative Properties to group.

Holt Algebra 1


Example 7: Dividing Numbers in Scientific Notation

Simplify and write the

answer in scientific notation

Write as a product of quotients.Simplify each quotient.

Simplify the exponent.Write 0.5 in scientific notation

as 5 x 10 .The second two terms have

the same base, so add the exponents.

Simplify the exponent.

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You can “split up” a quotient of products into a product of quotients:

Example:

Writing Math

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Simplify and write the answer in scientific notation.

Write as a product of quotients.Simplify each quotient.

Simplify the exponent.Write 1.1 in scientific notation

as 11 x 10 .The second two terms have

the same base, so add the exponents.


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Example 8: Application

The Colorado Department of Education spent about dollars in fiscal year 2004-05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form.

To find the average spending per student, divide the total debt by the number of students.

Write as a product of quotients.

Holt Algebra 1


Example 8 Continued

The Colorado Department of Education spent about dollars in fiscal year 2004-05 on public schools. There were about students enrolled in public school. What was the average spending per student? Write your answer in standard form.

To find the average spending per student, divide the total debt by the number of students.

The average spending per student is $5,800.

Simplify each quotient.


Write in standard form.

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In 1990, the United States public debt was about dollars. The population of the United States was about people. What was the average debt per person? Write your answer in standard form.

To find the average debt per person, divide the total debt by the number of people.

Write as a product of quotients.

Holt Algebra 1


In 1990, the United States public debt was about dollars. The population of the United States was about people. What was the average debt per person? Write your answer in standard form.

To find the average debt per person, divide the total debt by the number of people.

Check It Out! Example 8 Continued

Simplify each quotient.


Write in standard form.The average debt per person was $12,800.

Holt Algebra 1


Lesson Quiz: Part IFind the value of each expression.

1.

2.

3. The Pacific Ocean has an area of about 6.4 х 107

square miles. Its volume is about 170,000,000

cubic miles.

a. Write the area of the Pacific Ocean in standard

0.00293

3,745,000

form.

b. Write the volume of the Pacific Ocean in scientific notation. 1.7 108 mi3

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Lesson Quiz: Part II


4. Order the list of numbers from least to greatest

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Lesson Quiz: Part III

5. The islands of Samoa have an approximate area of 2.9 103 square kilometers. The area of Texas is about 2.3 102 times as great as that of the islands. What is the approximate area of Texas? Write your answer in scientific notation.

Holt Algebra 1


Lesson Quiz: Part IV

Simplify.

6. Simplify (3 1012) ÷ (5 105) and write the answer in scientific notation. 6 106

7. The Republic of Botswana has an area of 6 105 square kilometers. Its population is about 1.62 106. What is the population density of Botswana? Write your answer in standard form.

2.7 people/km2

Holt Algebra 1 7-2 Powers of 10 and Scientific Notation 7-2 Powers of 10 and Scientific Notation Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson.

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