# Numbers – Types & Definition

Want to download the Numbers – Types & Definition revision notes in PDF format?

[mathjax]Numbers are words, symbols or figures used in counting and making calculations. A number represents a particular quantity and indicates an order or sequence. It can be a sign number, fraction, surd and decimal.

### Types of Numbers

Integers
Integers are whole numbers, sign numbers and zero. Sign numbers are positive or negative numbers.

Sign Number
Positive numbers are numbers greater than zero such as 1, 2, 3 and so on. A positive number is signified by a “+” symbol.
Negative numbers are those with a value of less than zero. The symbol for negative numbers is “-“. The example of negative numbers are -1, -2, -3 and so on.

Rational Numbers
Rational numbers are numbers denoted as fractions or quotients of integers. Here are examples of rational numbers:
0.5 can be expressed as ½
0.001 as a fraction 1/1000
5 has a ratio of 5/1.

Irrational Numbers
Irrational numbers are numbers that cannot be expressed into a fraction and do not have exact decimals. An example of irrational numbers are the value of pi(π), and root such as $$\sqrt2$$ and $$\sqrt3$$ .

Real Number
A real number is the set of all types of a number including a rational and irrational number. It can be a fraction, counting number, negative number, zero and decimal.

Other Types of Number

Square Numbers
Square numbers are the product of a number multiplied by itself.
Example:
72 = 7 7 = 49

Surds
Surds are numbers inside radicals or the root of a number. It can be a square root, cube root or others.
Example:
$$\sqrt[3]{216}=6$$

Prime Numbers
The prime number are numbers that can only be divided by itself or 1. A prime number has a factor of 1 and itself.
Examples:
2, 3, 5, 7, 11 and so on.

Factor of a Number
The factor of a number are numbers whose product is equal to the given number and if divided will give an exact value.

Example:
Find the factor of 36.
a. 6 (6)= 36
b. 9(4) = 36
c. 3 (12) = 36
d. 2 (18) = 36
e. 1 (36) = 36

Another type of a factor is the prime factor. Prime factors are where the factor of a number is the product of prime numbers.

Example:
36 = 3 × 3 × 2 × 2
Notice that all the factors of 36 in this example are prime numbers. Getting factors this way is called Prime Factor Decomposition.

Example 2
Find the prime factor of  a^3b^2 = 200
200 = 25 (8) = 5 × 5 × 2 × 2 × 2
Therefore the value of a = 2 and b = 5.
$$2^35^2= 200$$

Least Common Multiple and Highest Common Factor
Least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. The number when divided to the given will give an exact number.
Example:
The LCM of 5, 4 and 2 is 20. If we divide 20 by either 5, 4 or 2, it will give us an exact number.

Highest Common Factor (HCF) are the highest number that can be divided into two or more numbers that will give an exact number.
Example:
Given 18 and 12.
The common factor of 18 and 12 are 1, 2, 3 and 6. Since 6 is the highest. The HCF is 6.

Simplifying an Expression
Sometimes an expression has multiple operations. To manipulate this, follow the BODMAS or  BIDMAS. BODMAS or BIDMAS stands for Brackets, Of or Indices, Division, Multiplication, Addition and Subtraction.
Steps in Solving

1. Brackets – First solve all inside the grouping symbols such as (), {} and [].
2. In order of operation, division, multiplication, add or subtract.

Example
3 + (50 – 5) ÷ 5 × 2 – 10
3 + (45) ÷ 5 × 2 – 10    Brackets
3 + 9 × 2 – 10             Division
3 + 18 – 10                Multiplication