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Number Systems

 

Numbers can be classified into various groups or sets:

  • The positive numbers are those greater than zero.They can be written with a ‘+’ in front such as +6, +2.4, +2/5, or they can be written without a sign, for example, 5, 7.3, 8/9

  • The negative numbers are those less than zero.Negative numbers are always written with a minus sign, ‘-‘ , in the front of it, for instance, -4, -0.65, -3/5.

  • The natural numbers, or counting numbers, are: 1, 2, 3, 4, 5.....

  • The whole numbers are the natural numbers, together with zero: 0, 1, 2, 3, 4, 5.....

  • If we consider the negative as well as positive whole numbers, these are known as the integers: -3, -2, -1, 0, 1, 2, 3.....

  • Through the introduction of fractions, the number system can be extended and all numbers that can be expressed in the form a/b, where ‘a’ and ‘b’ are integers and ‘b’ does not equal zero, are called rational numbers.This group will include the integers themselves since, for instance, 5 = 5/1 and -7 = -7/1 and so the integers can be expressed in the form a/b.

 

 

Exercise:

 

Work through the exercise below.  

Use these numbers to answer the questions:

 

-3,     7,     ¾,     +4,     723,     -½,     -1.75,     500,     +18,     0,

List:

  1. All the positive numbers

  2. All the natural numbers

  3. All the whole numbers

  4. All the negative numbers

  5. All the integers

  6. All the fractions

 

Answers below:

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  1. 7,+4, 723, 500, +18

  2. 7,+4, 723,500, +18

  3. 0,7, +4, 723,500, +18

  4. -3,-½, -1.75,

  5. 0, -3, 7, +4, 723, 500, +18

  6. -3, 7, +4, 723, -½, -1.75, 500, +18 (includes integers except 0 since they too can be expressed in the form a/b)

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