1. Warm Up California Standards Lesson Presentation Preview

2. Warm Up Order each set of numbers from least to greatest. 1. 10 , 10 , 10 , 10 2. 8 , 8 , 8 , 8 3. 2 , 2 , 2 , 2 4. 5.2 , 5.2 , 5.2 , 5.2 0 4 – 1 – 2 3 0 2 – 2 1 3 – 4 – 6 – 2 2 9 – 1 10 , 10 , 10 , 10 4 0 – 1 – 2 8 , 8 , 8 , 8 3 2 0 – 2 5.2 , 5.2 , 5.2 , 5.2 9 2 – 1 – 2 2 , 2 , 2 , 2 3 1 – 4 – 6

3. NS1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general. California Standards

4. Vocabulary scientific notation

6. You can find the product of a number and a power of 10 by moving the decimal point of the number. You may need to write zeros to the right or left of the number in order to move the decimal point.

7. A. 14  10 4 Multiply. 14.0 0 0 0 Since the exponent is a positive 4, move the decimal point 4 places to the right. Additional Example 1: Multiplying by Powers of Ten 140,000 B. 3.6  10  5 0 0 0 0 3.6 Since the exponent is a negative 5, move the decimal point 5 places to the left. 0.000036

8. A. 2.5  10 5 Multiply. 2.5 0 0 0 0 Since the exponent is a positive 5, move the decimal point 5 places to the right. Check It Out! Example 1 250,000 B. 10.2  10  3 0 10.2 Since the exponent is a negative 3, move the decimal point 3 places to the left. 0.0102

9. Powers of 10 are used when writing numbers in scientific notation. Scientific notation is a way to express numbers that are very large or very small. Numbers written in scientific notation are expressed as 2 factors. One factor is a number greater than or equal to 1. The other factor is a power of 10.

10. Additional Example 2: Writing Numbers in Scientific Notation Think: The number is less than 1, so the exponent will be negative. A. 0.00709 Think: The decimal needs to move 3 places to get a number between 1 and 10. Write the number in scientific notation. 7.09  10  3 So 0.00709 written in scientific notation is 7.09  10 –3 .

11. Additional Example 2: Writing Numbers in Scientific Notation Think: The number is greater than 1, so the exponent will be positive. B. 23,000,000,000 Think: The decimal needs to move 10 places to get a number between 1 and 10. Write the number in scientific notation. 2.3  10 10 So 23,000,000,000 written in scientific notation is 2.3  10 10 .

12. Check It Out! Example 2 Think: The number is less than 1, so the exponent will be negative. A. 0.000811 Think: The decimal needs to move 4 places to get a number between 1 and 10. Write the number in scientific notation. 8.11  10  4 So 0.000811 written in scientific notation is 8.11  10 –4 .

13. Check It Out! Example 2 Think: The number is greater than 1, so the exponent will be positive. B. 480,000,000 Think: The decimal needs to move 8 places to get a number between 1 and 10. Write the number in scientific notation. 4.8  10 8 So 480,000,000 written in scientific notation is 4.8  10 8 .

14. 1.35000 135,000 Think: Move the decimal right 5 places. A. 1.35  10 5 Additional Example 3: Reading Numbers in Scientific Notation Write the number in standard form. 1.35  10 5

15. 0002.7 Think: Move the decimal left 3 places. B. 2.7  10 –3 Write the number in standard form. Additional Example 3: Reading Numbers in Scientific Notation 0.0027 2.7  10 –3

16. 2.870000000 Think: Move the decimal right 9 places. A. 2.87  10 9 Write the number in standard form. Check It Out! Example 3 2,870,000,000 2.87  10 9

17. 000001.9 Think: Move the decimal left 5 places. B. 1.9  10 –5 Write the number in standard form. Check It Out! Example 3 0.000019 1.9  10 – 5

18. A certain cell has a diameter of approximately 4.11  10 -5 meters. A second cell has a diameter of 1.5  10 -5 meters. Which cell has a greater diameter? 4.11  10 -5 1.5  10 -5 Compare the exponents. Additional Example 4: Comparing Numbers in Scientific Notation Compare the values between 1 and 10. The first cell has a greater diameter. 4.11 > 1.5 Notice that 4.11  10 -5 > 1.5  10 -5 .

19. A star has a diameter of approximately 5.11  10 3 kilometers. A second star has a diameter of 5  10 4 kilometers. Which star has a greater diameter? 5.11  10 3 5  10 4 Compare the exponents. Check It Out! Example 4 The second star has a greater diameter. Notice that 3 < 4. So 5.11  10 3 < 5  10 4

20. Lesson Quiz Write each number in standard form. 1. 1.72  10 4 2. 6.9  10 –3 4 . 57,000,000 17,200 0.0069 3. 0.0053 Write each number in scientific notation. 5. Order the numbers from least to greatest. T 2  10 –4 , 9  10 –5 , 7  10 –5 7  10 –5 , 9  10 –5 , 2  10 –4 6. A human body contains about 5.6  10 6 microliters of blood. Write this number in standard notation. 5,600,000 5.3  10 –3 5.7  10 7