# Formula for Number System Questions

## Formulas for Number System

Number system is a method of representing  a number on the number line. A number system is a system of writing or expressing numbers. ### Formulas to Solve Number System

• Number system is a writing system for presenting number on the number line. A number system is a system of writing or expressing numbers.
• There are generally two type of Number
• Whole Number
• Natural Number.

### Number System Formulas & Definitions

• Natural Numbers
• All positive integers are called natural numbers. All counting numbers from 1 to infinity are natural numbers. N = {1, 2, 3, 4, 5, 6……….∞}
• Whole Numbers
• The set of numbers that includes all natural numbers and the number zero are called whole numbers. They are also called as Non-negative integers. W = { 0,1,2,3,4,5,6,7,8,…………..∞}
• Integers
• All numbers that do not have the decimal places in them are called integers. Z = {∞…….-3, -2, -1, 0, 1, 2, 3………∞}
• a. Positive Integers: 1, 2, 3, 4….. is the set of all positive integers.
• b. Negative Integers: −1, −2, −3….. is the set of all negative integers.
• c. Non-Positive and Non-Negative Integers: 0 is neither positive nor negative.
• Real Numbers
• All numbers that can be represented on the number line are called real numbers.
• Rational Numbers
• A rational number is defined as a number of the form a/b where ‘a’ and ‘b’ are integers and b ≠ 0. The rational numbers that are not integers will have decimal values. These values can be of two types
• a. Terminating decimal fractions: For example: $\frac{1}{5}$ = 0.5,$\frac{125}{4}$ = 31.25
• b. Non-Terminating decimal fractions: For example:$\frac{19}{6}$ = 3.1666666, $\frac{21}{9}$ = 2.33333
• Irrational Numbers
•  It is a number that cannot be written as a ratio $\frac{x}{y}$ form (or fraction). An Irrational numbers are non-terminating and non-periodic fractions. For example: $\sqrt{2}$ = 1.414
• Complex Numbers
• The complex numbers are the set {a+bi}, where, a and b are real numbers and ‘i’  is the imaginary unit.
• Imaginary Numbers
• A number does not exist on the number line is called imaginary number. For example square root of negative numbers are imaginary numbers. It is denoted by ‘i’ or ‘j.
• Even Numbers
• A number divisible by 2 is called an even number.
• For example: 2, 6, 8, 14, 18, 246, etc.
• Odd Numbers
• A number not divisible by 2 is called an odd number.
• For example: 3, 7, 9, 15, 17, 373, etc.
• Prime numbers
• A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself.
• For example: 2, 3, 5, 7, 11, 13, 17, etc.
• Composite numbers
• Numbers greater than 1 which are not prime, are known as composite numbers. For example: 4, 6, 8, 10, etc.

### Formulas for Number System and Basic Concept

1. (a – b)(a + b) = (a² – b²).
2. (a + b)² = (a² + b² + 2ab)
3. (a – b)² = (a² + b² – 2ab)
4. (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
5. (a³ + b³) = (a + b)(a² – ab + b²)
6.  (a³ – b³) = (a – b)(a² + ab + b²)
7. (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
8. When a + b + c = 0, then a³ + b³ + c³ = 3abc.

Read Also – How to solve number system problems Quickly

### Formulas for finding the Squares of a number .

• Squares of numbers 91-100:
• 972
Step 1: 100-97 = 3

Step 2: 97-3 = 94

Step 3: 32= 09

Final result: From step 2 and

Step 3  => 972= 9409

• 912

Step 1: 100-9 = 91

Step 2: 91-9 = 82

Step 3: 92 = 81

Final Result: From step 2 and step 3 => 912 = 8281

• Squares of numbers 100-109:
• 1022

Step 1: 102-100 = 2

Step 2: 102 +2 = 104

Step 3: 22 = 04 Final result:

From step 2 and step 3 => 1022=10404

• 1072

Step 1: 107-100 = 7

Step 2: 107+7 = 114

Step 3: 72 = 49

Final Result: From step 2 and step 3 => 1072 = 11449

• Squares of numbers 51-60
• 532

Step 1: 53-50 = 3

Step 2: 25+3 = 28

Step 3: 32 = 09

Final result: From step 2 and step 3 => 532 = 2809.

• 422

Step 1: 50-42 = 8

Step 2: 25-8 = 17

Step 3: 82 = 1764

Final Result From step 2 and step 3 => 422 = 1764

### 6 comments on “Formula for Number System Questions”

• Ashutosh Sinha

where can I find the squares material which was said in the number system video? 8
• HelpPrepInsta

Hello Ashutosh ,
we have resolved your concern regarding square.
we updated our page .

warm Regards
Prepinsta Team 14
• WatchToLearn

first formula is wrong a square minus b square is equal to a plus b into a -b 7
• PrepInsta

Actually its a cube minus b cube on the page, but although your formula is also correct. 3
• Ashish mark Daniel

1. (a – b) = (a² – b²) 11
• ten

superb well said 1