1. Holt Algebra 1 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

2. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Students will be able to: Evaluate and multiply by powers of 10 and convert between standard notation and scientific notation. Learning Targets

3. Holt Algebra 1 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.

4. Holt Algebra 1 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.

5. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation

6. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation 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. 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

7. Holt Algebra 1 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

8. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Find the value of each power of 10. a. 10 –2 c. 10 10 b. 10 5 10,000,000,000100,0000.01

9. Holt Algebra 1 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

10. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation 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. 0.0001C. 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.

11. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Write each number as a power of 10. a. 100,000,000 b. 0.0001c. 0.1

12. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation You can also move the decimal point to find the value of any number multiplied by a power of 10. You start with the number rather than starting with 1. Multiplying by Powers of 10

13. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Find the value of each expression. 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.

14. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Find the value of each expression. a. 853.4  10 5 853.4 0 0 0 0 85,340,000 b. 0.163  10 –2 0.0 0163

15. Holt Algebra 1 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.

16. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation 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.

17. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Write Saturn’s distance from the Sun in scientific notation. 1,427,000,000 9 places 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

18. Holt Algebra 1 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. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Use the information above to write Jupiter’s diameter in scientific notation. 143,000 km 1 4 3 0 0 0 5 places 1.43  10 5 km

20. Holt Algebra 1 7-2 Powers of 10 and Scientific Notation Use the information above to write Jupiter’s orbital speed in standard form. 1 3 0 0 0 13,000 m/s

21. Holt Algebra 1 7-2 Powers of 10 and 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