number system Topic-wise Practice Test, Examples With Solutions & More Shortcuts

Number Systems - Basic Formulas, Shortcuts, Rules, Tricks & Tips - Quantitative Aptitude

Useful For All Competitive Exams Like UPSC, SSC, BANK & RAILWAY

Posted By Careericons Team

Introduction to Number Systems:

In this article, We will help you understand better about expressing The Numbers, The Numerals and The Digits with Symbols. Lets discuss one by one

Numbers can be expressed in words and in numerals. The number 'three hundred and fifty-seven' is the word form and '357' is the numeral. Expressing a number in words is called numeration and representing a number in numerals is called notation. Just as all words are made up of alphabets, all numerals are built up of digits.

In our modern number system, we use ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 either individually or in combination with each other to build a numeral.

A system in which we study different types of numbers, their relationship and rules govern in them is called number system. In the Hindu-Arabic system, we use the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

These symbols are called digits. Out of these ten digits, 0 is called an insignificant digit, whereas the others are called significant digits.

What is Numerals?

A mathematical symbol representing a number in a systematic manner is called a numeral represented by a set of digits.

How to Write a Number?

To write a number, we put digits from right to left at the places designated as units, ten’s, hundred’s, thousand’s, ten thousand's, lakh’s, ten lakhs’, crore’s, ten crores’.

Let us see how the number 308761436 is denoted as,

It is read as "Thirty crore eighty-seven lakh sixty-one thousand four hundred thirty-six".

Number Systems - Types, Facts, Conversion Rules, Meanings & Definitions:

A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

The same sequence of symbols may represent different numbers in different numeral systems.

For example, "11" represents the number eleven in the decimal numeral system (used in common life), the number three in the binary numeral system (used in computers), and the number two in the unary numeral system (e.g. used in tallying scores).

A general example to help you remember patterns and spot the information you're looking. Here we give you a list of types of numbers with its definitons and examples.

Face & Place Values of the Digits in a Number

Numbers are named in terms of the place value system with base 10, in which the value of a digit depends on the place in which it is located in the numeral. The rightmost digit represents the unit's or one's place. Its place value is calculated by multiplying its face value (i.e., the digit itself) with 1.

The second digit from the right represents the ten's place. Its place value is calculated by multiplying its face value with 10. The third digit from the right represents the hundred's place, and so on.

The following table will be uesful for translating any number in numberical from ta word form.

What is Face Value ?

In a numeral, the face value of a digit is the value of the digit itself irrespective of its place in the numeral.

For example, In the numeral 486729, the face value of 8 is 8 the face value of 7 is 7, the face value of 6 is 6, the face value of 4 is 4 and so on.

What is Place (Local) Value ?

In a numeral, the place value of a digit changes according to the change of its place.

In a number,

1. Place value of unit's digit = (Digit at one’s place) x10⁰
2. Place value of ten's digit = (Digit at ten's place) x10¹
3. Place value of hundreds digit = (Digit at hundred’s place) x10²
4. Place value of thousand’s digit = (Digit at thousand’s place) x10³ and so on.
5. The place value of number is also called the local value of the number.

What is Place value of 5 in the number 15683,

Different Types of Numbers with Its Definitions & Examples

Number system is a mathematical presentation of numbers of a given set. For further discussion, let us understand number systems. There are various types of numbers,

Let us discuss the different divisions under the number system.

1. Natural Numbers

Natural numbers are counting numbers and these are denoted by N,

i.e.  N = {1,2,3……}

• All natural numbers are positive
• Zero is not a natural number, therefore 1 is the smallest natural number

2. Whole Numbers

All natural numbers and zero from the set of whole numbers and these are denoted by W,

i.e.  W = {0, 1, 2, 3…..}

• Zero is the smallest whole number
• Whole numbers are also called as non-negative integers

3. Integers

Whole numbers and negative numbers form the set of integers and these denoted by I,

i.e.  I = {……-4, -3, -2, -1, 0, 1, 2, 3, 4……}

Integers are of following two types

• Positive Integers

Natural numbers are called as positive integers and these are denoted by I⁺,

i.e.  I⁺ = (1, 2, 3, 4….}

• Negative Integers

Negative of natural numbers are called as negative integers and these are denoted by I^-

i.e.  I^- = (-1, -2, -3, -4,….}

Note: “0 is neither +ve nor –ve integer”

4. Even Numbers

A counting number, which is divisible by 2, is called an even number.

For example, 2, 4, 6, 8, 10, 12…… etc.

• The unit's place of every even number will be 0, 2, 4, 6 or 8

5. Odd Numbers

A counting number, which is not divisible by 2, is known as an odd number.

For example, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19…… etc.

• The unit’s place of every odd number will be 1, 3, 5, 7 or 9

6. Prime Numbers

A counting number is called a prime number when it is exactly divisible by only 1 and itself.

For example, 2, 3, 5, 7, 11, 13. etc.

• 2 is the only even number which is prime.
• A prime number is always greater than 1.
• 1 is not a prime number; therefore, the lowest odd prime number is 3.
• Every prime number greater than 3 can be represented by 6n + 1, where n is integer.

7. Composite Numbers

Composite numbers are non-prime natural numbers. They must have at least one factor apart from 1 and itself.

For example, 4, 6, 8, 9, etc.

• Composite number can be both Odd & Even numbers.
• 1 is neither a prime nor a composite number.

8. Co-primes

Two natural numbers are said to be co-primes, if their common divisor is 1.

For example, (9, 8) (12, 16), etc.

• Co-prime numbers may or may not be prime.
• Every pair of consecutive numbers is co-prime.

9. Rational Numbers

A number that can be expressed in the form of p/q is called a rational number. Where, p and q are integers and q ≠ 0

For example $7/5,2/9,6/4,\text"13"/\text"19"$ etc.

10. Irrational Numbers

The numbers that cannot be expressed in the form of p/q, are called irrational numbers, where p, q are integers and q ≠ 0.

For example $√2, √3, √7, √\text"11",$ etc.

• π is an irrational number as $22/7$ is not the actual value of , but it is its nearest value.
• Non-periodic infinite decimal fractions are called irrational numbers.

11. Real Numbers

Real numbers include both rational and irrational numbers. They are denoted by R,

For example, $5/9, √2, √7, π, 3/7,$ etc.

"9" - Important Aptitude Rules, Formulas & Quick Tricks to Solve Number System Based Aptitude Problems

In this list of rules, you will get an idea that How to solve all different types & kinds of Number System based aptitude problems asked in various competitive exams like UPSC, SSC, Bank, and Railway examinations at all levels.

By using this method, you can able to solve all problems from basic level to advanced level of questions asked based on Number System in a faster approch.

Let's discuss the rules one by one with all Number System Rules & Formulas with examples,

Rule 1:

If the sum of digits of two digit number is 'a' and if the digits or the number are reversed, such that number reduces by 'b', then

Rule 2:

If the sum of digits of two digit number is 'a' and if the digits of the number are reveresed, such that number increases by 'b', then,

Rule 3:

If the difference between a number and formed by number reversing digit is x, then the difference between both the digits of the number is $x/9$

Rule 4:

If the sum of a number and the number formed by reversing the digits is x, then the sum of digits of the number is $x/11$.

Rule 5:

Rule 6:

Rule 7:

Rule 8:

If n is a single digit number, then in $n^3$, n will be at unit place. It is valid for the number 0, 1, 4, 5, 6 or 9 As, digit at unit place in ($4^3$) is 4.

Rule 9:

If n is a single digit number then in $n^p$, where p is any number (+ve), n will be at unit place. It is valid for 5 and 6.

**More Types of Number System Based Aptitude Questions and Answers Practise Test With Online Quiz

Refer: Get all Topic-wsie Quantitative aptitude problems for upcoming competitive exams