1. Section 4.2 Place Value System

2. Objectives:  Understand and use the Babylonian System.  Understand and use the Hindu-Arabic Expanded Notation with addition and subtraction.  Use the Galley Method for multiplication.  Use Napier’s Rods for multiplication.

3. Key Terms:  Place Value System – the placement of the symbols in a numeral determines the value of the symbols, also called a positional system.  NOTE: In order to have a true place value system, you must have a symbol for zero.

4. Babylonian Number System  The Babylonians developed an early example of a place value system.  This system was based on powers of 60, called a sexagesimal system.  There are only 2 symbols in the Babylonian system:  Represents 1 -  Represents 10 -

5. For Example:  The number 23 can be written as:, however, for larger numbers, they used several symbols separated by spaces, and multiplied the value of these groups, of symbols, by increasing powers of 60.

6. Example 1:  Convert to Hindu-Arabic

7. Example 2:  Convert to Hindu-Arabic

8. Example 3:  Convert to Hindu-Arabic

9. Example 4: 7,717  Convert to Babylonian  In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

10. Example 5: 7,573  Convert to Babylonian  In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

11. Example 6: 128,485  Convert to Babylonian  In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

12. Section 4.2 Assignment I  Class work:  TB pg. 216/1 – 16 All  Remember you must write the problem and show ALL work to receive credit for this assignment.  NO work, NO grade!

13. Hindu-Arabic Numeration System Place Value  Based on Powers of 10.  Writing numbers in expanded notation.  6,582 = (6x10 3 )+(5x10 2 )+(8x10 1 )+(2x10 0 )

14. Example 7: 5,389  Write the number using expanded notation.

15. Example 8: 31,157  Write the number using expanded notation.

16. Example 9: 2,100,405  Write the number using expanded notation.

17. Section 4.2 Continued Addition and Subtraction using the Hindu- Arabic Expanded Notation

18. Example 10: 4,625 + 814  Add/Subtract using Expanded Notation

19. Example 11: 5,264 + 583  Add/Subtract using Expanded Notation

20. Example 12: 728 – 243  Add/Subtract using Expanded Notation

21. Example 13: 4,317 – 2,561  Add/Subtract using Expanded Notation

22. Section 4.2 Assignment II  Class work:  TB pg. 216/33 – 40 All  Remember you must write the problem and show ALL work to receive credit for this assignment.  NO work, NO grade!

23. Galley Method: 685 x 49  Begin by constructing a rectangle.

24. Galley Method: 685 x 49  Divide into triangles called a galley.

25. Galley Method: 685 x 49  Compute partial products in each box

26. Galley Method: 685 x 49  Add numbers along the diagonals.

27. Example 14: 7 x 364  Multiply using the Galley Method.

28. Example 15: 22 x 867  Multiply using the Galley Method.

29. Example 16: 239 x 456  Multiply using the Galley Method.

30. Napier’s Rods/Bones  Developed by John Napier in the 16 th Century, for doing multiplication.  TB pg. 215 The Napier's rods consist of strips of wood, metal or heavy cardboard and are three dimensional.

31. Example 17: 8 x 346  Using Napier’s Rods

32. Example 18: 21 x 768  Using Napier’s Rods

33. Example 19: 241 x 365  Using Napier’s Rods

34. Section 4.2 Assignment III  Class work:  TB pg. 216/41 – 52 All  Remember you must write the problem and show ALL work to receive credit for this assignment.  NO work, NO grade!