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 for Number System

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) = (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

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