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Section 4.3

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.

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Section 4.3

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  1. Section 4.3 Calculating in Other Bases

  2. 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.

  3. 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.

  4. 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.

  5. Example 1: 245 • List the number before and after the given number, in the given base.

  6. Example 2: 2045 • List the number before and after the given number, in the given base.

  7. Example 3: 678 • List the number before and after the given number, in the given base.

  8. Example 4: 1916 • List the number before and after the given number, in the given base.

  9. 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.

  10. Example 5: 245 • Convert to decimal (base ten) notation.

  11. Example 6: 40,3125 • Convert to decimal (base ten) notation.

  12. Example 7: 7,0368 • Convert to decimal (base ten) notation.

  13. 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.

  14. Example 8: 384 • Convert from decimal to base 5 Notation.

  15. Example 9: 645 • Convert from decimal to base 5 Notation.

  16. Example 10: 1838 • Convert from decimal to base 6 Notation.

  17. Section 4.3 Assignment • Class work: • Worksheet on teacher website

  18. Section 4.3 Part II Adding, Subtracting, Multiplying, and Dividing in Other Bases

  19. 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.”

  20. Addition Table for Base 5

  21. Example 11: Adding Base 5 • 3425 +2235

  22. Example 12: Adding Base 6 • 3156 +5246

  23. Example 13: Subtracting Base 5 • 4245 - 1435

  24. Example 14: Subtracting Base 6 • 3256- 1316

  25. 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.

  26. Multiplication Table for Base 5

  27. Example 15: Multiplying Base 5 • 345 x 425…..Use Galley Method

  28. Example 16: Multiplying Base 5 • 1345 x 325…..Use Galley Method

  29. Example 17:Division in Base 5 • 41325 235……..1st need to know multiples of 235

  30. Example 18:Division in Base 5 • 21435 325……..1st need to know multiples of 325

  31. Binary, Octal, and Hexadecimal Notation • TB pg. 226

  32. 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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