Homework 60: p.473: 17-45

Transcription

1 8.4: Scientific Notation Homework 60: p.473: 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] ] ] ] ] , ,

2 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.

3 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.

4 Why Tho?

5 Concept: Powers of 10

6 Example 1: Evaluating Powers of 10 Find the value of each power of 10. A B C Start with 1 and move the decimal point six places to the left Start with 1 and move the decimal point four places to the right. 10,000 Start with 1 and move the decimal point nine places to the right. 1,000,000,000

7 Student Led Example 1: Powers of 10 Find the value of each power of 10. a b c 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. 100,000 Start with 1 and move the decimal point ten places to the right. 10,000,000,000

8 Example 2: 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 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.

9 Student Led Example 2: Powers of 10 Write each number as a power of 10. a. 100,000,000 b 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.

10 Example 3: Multiplying by Powers of 10 Find the value of each expression. A ,389,000,000 B Move the decimal point 8 places to the right. Move the decimal point 3 places to the left.

11 Student Led Example 3: Multiplying by Powers of 10 Find the value of each expression. a Move the decimal point 5 85,340,000 places to the right. b Move the decimal point 2 places to the left.

12 Concept: Scientific Notation 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.

13 Calculator: Scientific Notation the Easy Way

14 Example 4: Dividing Numbers in Scientific Notation Simplify answer in scientific notation and write the 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.

15 Student Led Example 4: Dividing Numbers in SciNot Simplify answer in scientific notation. and write the 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.

16 Concept: Number Forms Standard Notation 1,000,000 Expanded Notation Exponential Notation 10 6 Scientific Notation

17 Example 5: Application The Colorado Department of Education spent about dollars in fiscal year 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.

18 Student Led Example 5: Application (Continued) The Colorado Department of Education spent about dollars in fiscal year 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. = = Simplify each quotient. Simplify the exponent. = 5800 Write in standard form. The average spending per student is $5800.

19 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. Write as a product of quotients.

20 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. Simplify each quotient. Simplify the exponent. Write in standard form. The average debt per person was $12,800.

21 End of Lesson Find the value of each expression ,745, The Pacific Ocean has an area of about 6.4 х 10 7 square miles. Its volume is about 170,000,000 cubic miles. a. Write the area of the Pacific Ocean in standard form. b. Write the volume of the Pacific Ocean in scientific notation mi 3