8.4: Scientific Notation

Homework 60: p.473: 17-45

Learning Objectives:

• Use Scientific Notation to represent extremely large and

extremely small numbers

Entry Task: Evaluate Each Expression (answer in standard notation) 1] 123 ⋅ 1,000

2] 123 ÷ 1,000

3] 0.003 ⋅ 100

4] 0.003 ÷ 100

5] 105

6] 10−4 7] 230

𝟏𝟐𝟑, 𝟎𝟎𝟎

𝟎. 𝟏𝟐𝟑

𝟎. 𝟑

𝟎. 𝟎𝟎𝟎𝟎𝟑

𝟏𝟎𝟎, 𝟎𝟎𝟎

𝟎. 𝟎𝟎𝟎𝟏

𝟏

Concept: Powers of 10

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.

Concept: Powers of 10

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.

Why Tho?

Concept: Powers of 10

Find the value of each power 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.

10,000 0.000001

Example 1: Evaluating Powers of 10

Find the value of each power of 10.

a. 10–2 c. 1010 b. 105

10,000,000,000 100,000 0.01

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.

Student Led Example 1: Powers of 10

Write each number as a power 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.

Example 2: Powers of 10

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.

Student Led Example 2: Powers of 10

Find the value of each expression.

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.

Example 3: Multiplying by Powers of 10

Find the value of each expression.

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.

Student Led Example 3: Multiplying by Powers of 10

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.

Concept: Scientific Notation

Calculator: Scientific Notation the Easy Way

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.

Example 4: 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 1.1 in scientific notation as 11 x 10 .

The second two terms have the same base, so add the exponents.

Simplify the exponent.

Student Led Example 4: Dividing Numbers in SciNot

Concept: Number Forms

Standard Notation

Expanded Notation

Exponential Notation

Scientific Notation

1,000,000

10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10

106

1 × 106

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.

Example 5: 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.

The average spending per student is $5800.

Simplify each quotient.

Simplify the exponent.

Write in standard form.

= 0.58 ×109–5

= 0.58 ×104

= 5800

Student Led Example 5: Application (Continued)

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.

Student Led Example 5: Application

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.

Simplify each quotient.

Simplify the exponent.

Write in standard form.

The average debt per person was $12,800.

Student Led Example 5: Application (continued)

Find 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

End of Lesson