Warm Up

1. Preview Warm Up California Standards Lesson Presentation

2. Warm Up Evaluate 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

3. 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. Vocabulary scientific notation

5. 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. 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.

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

9. Additional Example 1: Evaluating Powers of 10 Find the value of each power of 10. C. 109 A. 10–6 B. 104 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. Start with 1 and move the decimal point nine places to the right. 0.000001 10,000 1,000,000,000

10. Check It Out! Example 1 Find the value of each power of 10. b. 105 c. 1010 a. 10–2 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. 0.01 100,000 10,000,000,000

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

12. Additional Example 2: Writing Powers of 10 Write each number as a power of 10. B. 0.0001 C. 1000 A. 1,000,000 The decimal point is six places to the right of 1, so the exponent is 6. 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. Check It Out! Example 2 Write each number as a power of 10. b. 0.0001 c. 0.1 a. 100,000,000 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. Multiplying by Powers of 10 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.

15. Additional Example 3: Multiplying by Powers of 10 Find the value of each expression. A. 23.89  108 23.8 9 0 0 0 0 0 0 Move the decimal point 8 places to the right. 2,389,000,000 B. 467  10–3 Move the decimal point 3 places to the left. 4 6 7 0.467

16. Check It Out! Example 3 Find the value of each expression. a. 853.4  105 Move the decimal point 5 places to the right. 853.4 0 0 0 0 85,340,000 b. 0.163  10–2 Move the decimal point 2 places to the left. 0.0 0163 0.00163

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

19. 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. Move the decimal point 5 places to the right. 1 2 0 0 0 0 120,000 km

20. Additional Example 4B: Astronomy Application Saturn has a diameter of about km. Its distance from the Sun is about 1,427,000,000 km. Write Saturn’s distance from the Sun in scientific notation. Count the number of places you need to move the decimal point to get a number between 1 and 10. 1,427,000,000 1,4 2 7,0 0 0,0 0 0 9 places Use that number as the exponent of 10. 1.427  109 km

21. Check It Out! Example 4a Jupiter has a diameter of about 143,000 km. Write Jupiter’s diameter in scientific notation. Count the number of places you need to move the decimal point to get a number between 1 and 10. 143,000 km 1 4 3 0 0 0 5 places Use that number as the exponent of 10. 1.43  105 km

22. Check It Out! Example 4b Jupiter’s orbital speed is approximately 1.3 × 104 m/s. Write Jupiter’s orbital speed in standard form. 1.3 × 104 m/s 1 3 0 0 0 Move the decimal point 4 places to the right. 13,000 m/s

23. Additional Example 5: Comparing and Ordering Numbers in Scientific Notation 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.

24. Check It Out! Example 5 Order the list of numbers from least to greatest. Step 1 List the numbers in order by powers of 10. 2  10-12, 4  10-3, 5.2  10-3, 3  1014, 4.5  1014, 4.5  1030 Step 2 Order the numbers that have the same power of 10.

25. Lesson Quiz: Part I 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 3,745,000 0.00293 form. b. Write the volume of the Pacific Ocean in scientific notation. 1.7  108 mi3

26. , Lesson Quiz: Part II Find the value of each expression. 4. Order the list of numbers from least to greatest.