1. Test on Numbers Thursday 7 th October Surds Index laws Cubes and Squares Scientific Notation

2. Quick Revisit- Surds 12 10

3. Quick check Index Laws

4. Order each set of numbers from least to greatest ( ascending order)

5. Order each set of numbers from least to greatest ( ascending order)- solutions

8. POWERS of 10

11. Write 6 million as power of 10 Write 20000 as power of 10 Write 15000 as power of 10

12. An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notation is a shorthand way of writing such numbers.

13. The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint In scientific notation the number of atoms in a penny is 2.0  10 22, and the size of each atom is 3.0  10 –8 centimeters across. An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across.

15. Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. 0.00709 Move the decimal to get a number between 1 and 10. 7.09 7.09  10 Set up scientific notation. Think: The decimal needs to move 3 places. Check 7.09  10 –3 = 7.09  0.001 = 0.00709 Write 0.00709 in scientific notation. So 0.00709 written in scientific notation is 7.09  10 –3.

16. Try This: Example 2 Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. 0.000811 Move the decimal to get a number between 1 and 10. 8.11 8.11  10 Set up scientific notation. Think: The decimal needs to move 4 places. Check 8.11  10 = 8.11  0.0001 = 0.000811 –4 Write 0.000811 in scientific notation. So 0.000811 written in scientific notation is 8.11  10 –4.

17. A pencil is 18.7 cm long. If you were to lay 10,000 pencils end to end, how many millimeters long would they be? Write the answer in scientific notation. 187 mm  10,000 1 centimeter = 10 millimeters, so 18.7 centimeters = 187 millimeters Find the total length. 1,870,000 mm Additional Example 3: Application

18. Think: The decimal needs to move 6 places. The 10,000 pencils would be 1.87  10 6 mm long, laid end to end. This is about one mile long. Additional Example 3 Continued 1.87  10 Set up scientific notation. Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive. 1,870,000 mm

19. An oil rig can hoist 2,400,000 pounds with its main derrick. It distributes the weight evenly between 8 wire cables. What is the weight that each wire cable can hold? Write the answer in scientific notation. 2,400,000 pounds ÷ 8 cables = 300,000 pounds per cable Each cable can hold 300,000 pounds. Try This: Example 3 Find the weight each cable is expected to hold by dividing the total weight by the number of cables. Now write 300,000 pounds in scientific notation.

20. Think: The decimal needs to move right to change 3.0 to 300,000, so the exponent will be positive. Think: The decimal needs to move 5 places. Each cable can hold 3.0  10 pounds. 5 3.0  10 Set up scientific notation. Try This: Example 3 Continued

21. Multiplying and Dividing numbers in Scientific Notation form What is the product of: And (use index laws) and express answer in SN

22. X Same base, different exponent or index If same base number, add the index Write them out so that same base numbers are next to each other Multiply the whole numbers

23. Dividing numbers in SN form 1. Rewrite it as one over the other 2. Use index laws: if dividing same base numbers, subtract the indices 3. Complete operation with index numbers 4. Divide whole numbers

24. Lesson Quiz Write in standard notation. 1. 1.72  10 4 2. 6.9  10 –3 4. 57,000,000 17,200 0.0069 3. 0.0053 5.3  10 –3 5.7  10 7 Write in scientific notation. 5. A human body contains about 5.6 x 10 6 microliters of blood. Write this number in standard notation. 5,600,000

25. 6. Evaluate and express in SN 7. Evaluate and express in SN

26. 135,000 1.35  100,000 Think: Move the decimal right 5 places. A. 1.35  10 5 1.35  10 5 10 = 100,000 5 Additional Example 1A: Translating Scientific Notation to Standard Notation Write the number in standard notation.

27. 2,870,000,000 2.87  1,000,000,000 Think: Move the decimal right 9 places. A. 2.87  10 9 2.87  10 9 10 = 1,000,000,000 9 Write the number in standard notation. Try This: Example 1A

28. 0.0027 Divide by the reciprocal. 2.7  100 Think: Move the decimal left 3 places. 2.7  10 –3 B. 2.7  10 –3 10 = –3 1 100 2.7  1 100 Write the number in standard notation. Additional Example 1B: Translating Scientific Notation to Standard Notation Continued

29. C. –2.01  10 4 –20,100 Think: Move the decimal right 4 places. –2.01  10 4 10 = 10,000 4 –2.01  10,000 Additional Example 1C: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation.

30. 1.9  10,000 0.000019 Divide by the reciprocal. Think: Move the decimal left 5 places. 1.9  10 –5 B. 1.9  10 –5 –5 1 10 = 10,000 Write the number in standard notation. 1.9  1 10,000 Try This

31. 10 = 100,000,000 8 –5.09  10 8 –5.09  100,000,000 C. –5.09  10 8 Write the number in standard notation. Try This –509,000,000 Think: Move the decimal right 8 places.

32. Write 28750.9 in scientific notation. 1. 2.87509 x 10 -5 2. 2.87509 x 10 -4 3. 2.87509 x 10 4 4. 2.87509 x 10 5

33. Write (2.8 x 10 3 )(5.1 x 10 -7 ) in scientific notation. 1. 14.28 x 10 -4 2. 1.428 x 10 -3 3. 14.28 x 10 10 4. 1.428 x 10 11

34. Write 531.42 x 10 5 in scientific notation. 1..53142 x 10 2 2. 5.3142 x 10 3 3. 53.142 x 10 4 4. 531.42 x 10 5 5. 53.142 x 10 6 6. 5.3142 x 10 7 7..53142 x 10 8