Section 4.2Place Value System

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.

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.

Babylonian Number SystemThe 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 -

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.

Example 1:Convert to Hindu-Arabic

Example 2:Convert to Hindu-Arabic

Example 3:Convert to Hindu-Arabic

Example 4: 7,717Convert to Babylonian

In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

Example 5: 7,573Convert to Babylonian

In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

Example 6: 128,485Convert to Babylonian

In order to convert, we need to divide by 60, similar to converting seconds to hours and minutes.

Section 4.2 Assignment IClass 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!

Hindu-Arabic Numeration System Place Value

Based on Powers of 10.

Writing numbers in expanded notation.

6,582 = (6x103)+(5x102)+(8x101)+(2x100)

Example 7: 5,389Write the number using expanded

notation.

Example 8: 31,157Write the number using expanded

notation.

Example 9: 2,100,405Write the number using expanded

notation.

Section 4.2 ContinuedAddition and Subtraction using the Hindu-Arabic Expanded Notation

Example 10: 4,625 + 814Add/Subtract using Expanded

Notation

Example 11: 5,264 + 583Add/Subtract using Expanded

Notation

Example 12: 728 – 243 Add/Subtract using Expanded

Notation

Example 13: 4,317 – 2,561 Add/Subtract using Expanded

Notation

Section 4.2 Assignment IIClass 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!

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

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

Galley Method: 685 x 49Compute partial products in each

box

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

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

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

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

Napier’s Rods/BonesDeveloped by

John Napier in the 16th Century, for doing multiplication. TB pg. 215

The Napier's rods consist of strips of wood, metal or heavy cardboard and are three dimensional.

Example 17: 8 x 346Using Napier’s Rods

Example 18: 21 x 768Using Napier’s Rods

Example 19: 241 x 365Using Napier’s Rods

Section 4.2 Assignment IIIClass 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!