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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.

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section 4 3

Section 4.3

Calculating in Other Bases

objectives
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
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
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 24 5
Example 1: 245
  • List the number before and after the given number, in the given base.
example 2 204 5
Example 2: 2045
  • List the number before and after the given number, in the given base.
example 3 67 8
Example 3: 678
  • List the number before and after the given number, in the given base.
example 4 19 16
Example 4: 1916
  • List the number before and after the given number, in the given base.
section 4 3 assignment
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 24 5
Example 5: 245
  • Convert to decimal (base ten) notation.
example 6 40 312 5
Example 6: 40,3125
  • Convert to decimal (base ten) notation.
example 7 7 036 8
Example 7: 7,0368
  • Convert to decimal (base ten) notation.
section 4 3 assignment1
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
Example 8: 384
  • Convert from decimal to base 5 Notation.
example 9 645
Example 9: 645
  • Convert from decimal to base 5 Notation.
example 10 1838
Example 10: 1838
  • Convert from decimal to base 6 Notation.
section 4 3 assignment2
Section 4.3 Assignment
  • Class work:
    • Worksheet on teacher website
section 4 3 part ii
Section 4.3 Part II

Adding, Subtracting, Multiplying, and Dividing in Other Bases

slide20
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.”
section 4 3 assignment ii
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
Example 15: Multiplying Base 5
  • 345 x 425…..Use Galley Method
example 16 multiplying base 5
Example 16: Multiplying Base 5
  • 1345 x 325…..Use Galley Method
example 17 division in base 5
Example 17:Division in Base 5
  • 41325 235……..1st need to know multiples of 235
example 18 division in base 5
Example 18:Division in Base 5
  • 21435 325……..1st need to know multiples of 325
section 4 3 assignment ii1
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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