Test on Numbers

1. Test on Numbers Thursday 7th 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 notationis a shorthand way of writing such numbers.

13. Helpful Hint 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. In scientific notation the number of atoms in a penny is 2.0  1022, 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. 7.09  10 So 0.00709 written in scientific notation is 7.09  10–3. Check 7.09  10–3 = 7.09  0.001 = 0.00709 Translating Standard Notation to Scientific Notation Write 0.00709 in scientific notation. Move the decimal to get a number between 1 and 10. 0.00709 7.09 Set up scientific notation. Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. Think: The decimal needs to move 3 places.

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

17. Additional Example 3: Application 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. 1 centimeter = 10 millimeters, so 18.7 centimeters = 187 millimeters 187 mm  10,000 Find the total length. 1,870,000 mm

18. 1.87  10 Additional Example 3 Continued 1,870,000 mm 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. Think: The decimal needs to move 6 places. The 10,000 pencils would be 1.87  106 mm long, laid end to end. This is about one mile long.

19. Try This: Example 3 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. Find the weight each cable is expected to hold by dividing the total weight by the number of cables. 2,400,000 pounds ÷ 8 cables = 300,000 pounds per cable Each cable can hold 300,000 pounds. Now write 300,000 pounds in scientific notation.

20. 3.0  10 5 Each cable can hold 3.0  10 pounds. Try This: Example 3 Continued Set up scientific notation. 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.

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 Write them out so that same base numbers are next to each other If same base number, add the index 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. 5.3  10–3 5.7  107 Lesson Quiz Write in standard notation. 1. 1.72  104 17,200 2. 6.9  10–3 0.0069 Write in scientific notation. 3. 0.0053 4. 57,000,000 5. A human body contains about 5.6 x 106 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. 1.35  10 5 5 10 = 100,000 Additional Example 1A: Translating Scientific Notation to Standard Notation Write the number in standard notation. A. 1.35  105 1.35  100,000 Think: Move the decimal right 5 places. 135,000

27. 2.87  10 9 10 = 1,000,000,000 9 Try This: Example 1A Write the number in standard notation. A. 2.87  109 2.87  1,000,000,000 2,870,000,000 Think: Move the decimal right 9 places.

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

29. 4 4 10 = 10,000 –2.01  10 –2.01  10,000 Additional Example 1C: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation. C. –2.01  104 –20,100 Think: Move the decimal right 4 places.

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

31. 8 –5.09  10 8 10 = 100,000,000 Try This Write the number in standard notation. C. –5.09  108 –5.09  100,000,000 –509,000,000 Think: Move the decimal right 8 places.

32. Write 28750.9 in scientific notation. • 2.87509 x 10-5 • 2.87509 x 10-4 • 2.87509 x 104 • 2.87509 x 105

33. Write (2.8 x 103)(5.1 x 10-7) in scientific notation. • 14.28 x 10-4 • 1.428 x 10-3 • 14.28 x 1010 • 1.428 x 1011

34. Write 531.42 x 105 in scientific notation. • .53142 x 102 • 5.3142 x 103 • 53.142 x 104 • 531.42 x 105 • 53.142 x 106 • 5.3142 x 107 • .53142 x 108