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**.

### Decimal Number:

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

**Example:** 27.45

### 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.

### Number:

Group of digits is called as a number.

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

### 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

### 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

### 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…

### 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...

Speed Addition Tricks

### 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...

### 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

### 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

### 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

### 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

### Odd Numbers:

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

**Example:** 1, 3,5,7,9…

**Formula:** n / 2 ≠ 0

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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...