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SS1: MATHEMATICS - 1ST TERM

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  1. Number Base System I | Week 1
    6Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3Topics
    |
    1 Quiz
  3. Number Base System III | Week 3
    2Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2Topics
  5. Modular Arithmetic II | Week 5
    2Topics
  6. Modular Arithmetic III | Week 6
    3Topics
    |
    1 Quiz
  7. Indices I | Week 7
    2Topics
  8. Indices II | Week 8
    1Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3Topics
  10. Logarithms II
    1Topic
    |
    1 Quiz
Lesson 1, Topic 3
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Converting Numbers in Base Ten to other Bases

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This involves the successive division of the base ten by the required base. The remainders are recorded for each division at each step of the division until the division is completed. Finally, you are to collect all the remainders from the final to the first.

Example 1

Express 224ten in 

(i) Binary

(ii) Octal

(iii) Hexadecimal

Solution

(i)

Binary = 2

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 Answer ⇒ 224ten = 111000002

Solution (ii)

Octal = 8

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Answer ⇒ 224ten = 340eight 

(iii)

Hexadecimal = 16

Screen Shot 2021 10 23 at 9.52.57 PM

Note: 14 = E

Answer ⇒ 224ten = E0sixteen

Example 2

Express 674.235ten in base 8.

Solution:

Whole Number Part

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674ten = 1242eight

Decimal part can be converted to base 8

(a) 0.235 x 8 = 1.88

(b) Multiply 0.88 by 8 i.e. 0.88  x 8 = 7.04

(c) Multiply 0.04 by 8 i.e. 0.04  x 8 = 0.32

(d) Multiply 0.32 by 8 i.e. 0.32  x 8 = 2.56

(e) The answer is the whole numbers written out downwards

i.e. 0.235ten = 0.1702eight 

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