1. 7-2 Powers of 10 and Scientific Notation Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview

2. 7-2 Powers of 10 and Scientific Notation Warm Up Evaluate each expression. 1. 123  1,000 2. 123  1,000 3. 0.003  100 4. 0.003  100 5. 10 4 6. 10 –4 7. 23 0 123,000 0.123 0.3 0.00003 10,000 0.0001 1

3. 7-2 Powers of 10 and Scientific Notation 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents. California Standards

4. 7-2 Powers of 10 and Scientific Notation scientific notation Vocabulary

5. 7-2 Powers of 10 and Scientific Notation 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.

6. 7-2 Powers of 10 and Scientific Notation 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.

7. 7-2 Powers of 10 and Scientific Notation

8. 7-2 Powers of 10 and Scientific Notation 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

9. 7-2 Powers of 10 and Scientific Notation Find the value of each power of 10. Additional Example 1: Evaluating Powers of 10 Start with 1 and move the decimal point six places to the left. A. 10 –6 C. 10 9 B. 10 4 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

10. 7-2 Powers of 10 and Scientific Notation Check It Out! Example 1 Find the value of each power of 10. a. 10 –2 c. 10 10 b. 10 5 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.

11. 7-2 Powers of 10 and Scientific Notation If you do not see a decimal point in a number, it is understood to be at the end of the number. Reading Math

12. 7-2 Powers of 10 and Scientific Notation Write each number as a power of 10. Additional 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. 0.0001C. 1000 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.

13. 7-2 Powers of 10 and Scientific Notation Check It Out! Example 2 Write each number as a power of 10. a. 100,000,000 b. 0.0001c. 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.

14. 7-2 Powers of 10 and Scientific Notation You can also move the decimal point to find the product of any number and a power of 10. You start with the number instead of starting with 1. Multiplying by Powers of 10

15. 7-2 Powers of 10 and Scientific Notation Find the value of each expression. Additional Example 3: Multiplying by Powers of 10 A. 23.89  10 8 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.

16. 7-2 Powers of 10 and Scientific Notation Check It Out! Example 3 Find the value of each expression. a. 853.4  10 5 853.4 0 0 0 0 Move the decimal point 5 places to the right. 85,340,000 b. 0.163  10 –2 0.0 0163 Move the decimal point 2 places to the left.

17. 7-2 Powers of 10 and 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.

18. 7-2 Powers of 10 and Scientific Notation Standard form refers to the usual way that numbers are written—not in scientific notation. Reading Math

19. 7-2 Powers of 10 and Scientific Notation Additional 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.

20. 7-2 Powers of 10 and Scientific Notation Write Saturn’s distance from the Sun in scientific notation. 1,427,000,000 9 places Additional 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  10 9 km

21. 7-2 Powers of 10 and Scientific Notation Check It Out! Example 4a Jupiter has a diameter of about 143,000 km. 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  10 5 km

22. 7-2 Powers of 10 and Scientific Notation Check It Out! Example 4b Jupiter’s orbital speed is approximately 1.3 × 10 4 m/s. 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 1.3 × 10 4 m/s

23. 7-2 Powers of 10 and Scientific Notation Order the list of numbers from least to greatest. Additional 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.

24. 7-2 Powers of 10 and Scientific Notation Order the list of numbers from least to greatest. Check It Out! Example 5 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  10 14, 4.5  10 14, 4.5  10 30

25. 7-2 Powers of 10 and Scientific Notation Lesson Quiz: Part I Find the value of each expression. 1. 2. 3. 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 0.00293 3,745,000 form. b. Write the volume of the Pacific Ocean in scientific notation. 1.7  10 8 mi 3

26. 7-2 Powers of 10 and Scientific Notation Lesson Quiz: Part II Find the value of each expression. 4. Order the list of numbers from least to greatest.,