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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
- (a – b)(a + b) = (a² – b²).
- (a + b)² = (a² + b² + 2ab)
- (a – b)² = (a² + b² – 2ab)
- (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
- (a³ + b³) = (a + b)(a² – ab + b²)
- (a³ – b³) = (a – b)(a² + ab + b²)
- (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
- 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
where can I find the squares material which was said in the number system video?
Hello Ashutosh ,
we have resolved your concern regarding square.
we updated our page .
warm Regards
Prepinsta Team
first formula is wrong a square minus b square is equal to a plus b into a -b
Actually its a cube minus b cube on the page, but although your formula is also correct.
1. (a – b) = (a² – b²)
superb well said