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## PowerPoint Slideshow about ' Section 4.3' - whitney

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### Section 4.3

Calculating in Other Bases

Objectives

- Change numerals in bases other than ten to base ten.
- Change base ten numerals to numerals in other bases.
- Add and Subtract in bases other than ten.
- Multiply and Divide in bases other than ten.

Key Terms

- Digital – a word used in computer technology and refers to a method of encoding numbers, letters, visual images, and sounds using a base two system.
- Binary – base two system.
- Octal System – base eight.
- Hexadecimal System – base sixteen.

Background

- As you have seen, so far, most numeral systems are based on powers of ten, except for the Babylonian and Mayan system.
- Babylonian system based on powers of 60.
- Mayan system based on powers of 20.
- Other societies around the world, including ours, use bases 2, 3, 4, 5, or 8.
- Computers, DVD players, and cell phones use bases 2, 8, and 16.

Example 1: 245

- List the number before and after the given number, in the given base.

Example 2: 2045

- List the number before and after the given number, in the given base.

Example 3: 678

- List the number before and after the given number, in the given base.

Example 4: 1916

- List the number before and after the given number, in the given base.

Section 4.3 Assignment

- Class work:
- TB pg. 228/1 – 10
- Remember you must write the problem and show ALL work, when necessary, to receive credit for the assignment.

Example 5: 245

- Convert to decimal (base ten) notation.

Example 6: 40,3125

- Convert to decimal (base ten) notation.

Example 7: 7,0368

- Convert to decimal (base ten) notation.

Section 4.3 Assignment

- Class work:
- TB pg. 228/12 – 22
- Remember you must write problems and show ALL work to receive credit for the assignment.

Example 8: 384

- Convert from decimal to base 5 Notation.

Example 9: 645

- Convert from decimal to base 5 Notation.

Example 10: 1838

- Convert from decimal to base 6 Notation.

Section 4.3 Assignment

- Class work:
- Worksheet on teacher website

Section 4.3 Part II

Adding, Subtracting, Multiplying, and Dividing in Other Bases

NOTE:

- “If you thoroughly understand the concept of place value in our Hindu-Arabic numeration system, then you can easily modify the techniques…to compute in other place value systems.”

Example 11: Adding Base 5

- 3425 +2235

Example 12: Adding Base 6

- 3156 +5246

Example 13: Subtracting Base 5

- 4245 - 1435

Example 14: Subtracting Base 6

- 3256- 1316

Section 4.3 Assignment II

- Class work:
- TB pg. 229/44 – 56 Even
- Remember you must write problems and show ALL work to receive credit for this assignment.

Example 15: Multiplying Base 5

- 345 x 425…..Use Galley Method

Example 16: Multiplying Base 5

- 1345 x 325…..Use Galley Method

Example 17:Division in Base 5

- 41325 235……..1st need to know multiples of 235

Example 18:Division in Base 5

- 21435 325……..1st need to know multiples of 325

Binary, Octal, and Hexadecimal Notation

- TB pg. 226

Section 4.3 Assignment II

- Class work:
- Worksheet Online
- Multiplying and Dividing in other Bases
- Remember you must show ALL work to receive credit for the assignment.

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