An **arithmetical number** can express by a word, symbol, or figure. Those are representing a particular quantity and used in counting, measuring and **making calculations**.

We covered almost all number classifications for Competitive exam point of view. These number classifications are necessary to learn for **numerical aptitude**.

**Note: **Click on show/hide button to show index of the content.

1. Decimal Number

2. Digit

3. Number

4. Face Value

5. Place Value

6. Natural Numbers (N)

7. Whole Numbers (W)

8. Integers(Z)

9. Rational Numbers (Q)

10. Irrational Numbers (P)

11. Real Numbers(R)

12. Even Numbers

13. Odd Numbers

14. Prime Numbers

15. Composite Numbers

16. Co-Primes Numbers

17. Twin prime numbers

18. Consecutive numbers

19. Consecutive even numbers
20. Consecutive odd numbers
21. Complex Number

Speed Addition Tricks

### 1. Decimal Number:

Decimal number contains decimal point. Decimal point is **.**

**Example:** 27.45

### 2. Digit:

Classification of number system 0, 1, 2,3,4,5,6,7,8 and 9 symbols are called **digits**.

**Example:**0,1,2,3,4,5,6,7,8,9.

### 3. Number:

Group of digits is called as a number.

**Example:** 21, 456, 1244, 25734 etc

### 4. Face Value:

Face value is nothing but actual value of the digit.

**Example: ** 458

Face value of 4 is 4

Face value of 5 is 5

Face value of 8 is 8

### 5. Place Value:

When the value contains digits that is **number**, such digits counting is units, tens, hundreds, thousands…etc

**Example: **342

The place of 2 is units. Place value of 2 * 1 = 2

The place of 4 is tens. Place value of 4 * 10 = 40

The place of 3 is Hundreds. Place value of 3 * 100 = 300

### 6. Natural Numbers (N):

Counting numbers without zero is called natural numbers. Natural numbers does not contain zero. Natural numbers denoted by N

**Formula: **n > 0

**Example: **1,2,3,4,5,6,7,8,9,10,11,12…

### 7. Whole Numbers (W):

Counting numbers with zero is called as **whole numbers**. Whole numbers denoted by **W**.

**Formula:** n ≥ 0

Whole numbers = Natural numbers + zero

**Example: **0,1,2,3...

### 8. Integers(Z):

Counting Numbers with zero and –ve numbers is called as **integers**. All integers are fractions. **Not all fractions are integers**. Integers denoted by **Z**

**Positive Integers:**n > 0; [1, 2, 3...]**Negative Integers:**n < 0; [-1,-2,-3...]**Non-Positive Integers:**n ≤ 0; [0,-1,-2,-3...]**Non-Negative Integers:**n ≥ 0; [0, 1, 2, 3...]

**Formula:** n ≥ 0 or n ≤ 0

Integers = Whole numbers + the negative of the whole numbers.

**Example:** ….3,-2,-1, 0,1,2,3...

### 9. Rational Numbers (Q):

Rational numbers nothing but **fraction of real number**. Rational numbers denoted by **Q**. Fractions can be written as a **terminating decimal** or a **repeating decimal**.

**Example:** 22/7, 45/6…

**Formula:** m/n remainder is not zero

Rational numbers = Integers + fractions

### 10. Irrational Numbers (P):

irrational number is a number that **perfectly divisible by itself**. Irrational Numbers is denoted by **P**.Irrational numbers are numbers that cannot be written as a **fraction**. Another way to see them is that they are **neither repeating decimals nor terminating decimals**.

**Example:** 22/2, 45/5…

**Formula:** m/n remainder is zero

### 11. Real Numbers(R):

Collection of rational and irrational numbers called as **real numbers**. Real number is denoted by **R**.

**Example:** 22/2, 45/5, 22/2, 45/5…

**Formula:** m/n

Real numbers = rational numbers + irrational numbers

### 12. Even Numbers:

A number perfectly divisible by 2 is called as **even number**. Alternative numbers from zero is also called as **even numbers**.

**Example: **0, 2, 4,6,8,10,12…

**Formula:**n / 2 = 0

### 13. Odd Numbers:

A number not perfectly divisible by 2 is called as **odd number**.

**Example:** 1, 3,5,7,9…

**Formula:** n / 2 ≠ 0

### 14. Prime Numbers:

Numbers which is divisible by itself and 1 is called as **prime numbers**. 1 is not a prime number.

**Example:** 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 89, 97

**1Q:** How to check 157 is prime number or not?

**Solution: **

**Step 1 :** 13 > √157

**Step 2 :** Prime numbers less than 13. So less than 13 prime numbers are 2, 3, 5, 7 and 11.

**Step 3 :** 157 is not divisible by any prime numbers (below 13).

**Result :** Finally 157 is a prime number.

**Formula:** n/n, n/1

### 15. Composite Numbers:

non prime numbers are called **composite prime numbers**. 1 is neither a prime number nor a composite number. 2 is the only **even prime number**.

**Example:** 4, 6, 8, 9….

**Formula:** Natural numbers- prime numbers

### 16. Co-Primes Numbers:

Two natural numbers are **co-primes** if their H.C.F. is 1. For example, (2, 3), (4, 5) are co-primes.

**Example:** (2,3), (4,5),(4,9), (21,44)..

**Formula:** 2 number H.C.F is 1

### 17. Twin prime numbers:

A pair of prime numbers difference is two are called **twin prime number**.

**Example:** The twin prime numbers between 1 and 100.

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73).

**Formula:** n2-n1=2

### 18. Consecutive numbers:

If the difference between two numbers is 1, it is called as **consecutive number**.

**Formula:** x, x+1, x+2

**Example:** 16,17,18,19

### 19. Consecutive even numbers:

if the difference between two numbers is 2, it is called as **consecutive even numbers**.

**Formula:** x, x+2, x+4

**Example:** 16, 18, 20

### 20. Consecutive odd numbers:

if the difference between two numbers is 2, it is called as **consecutive odd numbers**.

**Formula:** x, x+2, x+4

**Example:** 17, 19, 21

### 21. Complex Number:

A Complex Number is a **combination of Real Number and Imaginary Number**. Complex number is denoted by **Im(z)**.

**Formula:** a + bi

a, b real numbers

I imaginary number.

**Example:**
√(-7), √(1-8), √(-25) = 5i, etc...