# Number Systems

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• 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

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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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