what is number system
Answers
Step-by-step explanation:
Number system is way of representing numbers in different symbol based on type of system.
Different types of Number System
1. Binary Number System
A binary number system is a system which has a base of two. It means that it has only 2 different symbols that make up its number system.
The 2 symbols are
The numbers that are made in Binary Number System are made up of 0 or 1.
2. Decimal Number System
The number system that we follow is called as Decimal Number System where the base is 10.The base 10 indicates that there are 10 different symbols that we use.
The ten symbols are:
These symbols are called as digits.
Any number that we form is a combination of the above digits,
1425 – Combination of 1, 2, 3, 4,
494737 – Combination of 4, 9, 4, 7, 3, 7
The number 1486 can be represented as
We represent the numbers in this manner because we are using different digits and each digit has a different place value depending on its position.
The representation should be in the power of 10’s.
Any two digit ‘a’ and ‘b’ can be represented as
Three digits a, b and c should be represented as
A decimal number system has 10 digits but it consists of infinite numbers.
Real Numbers:
Real numbers represent the actual physical quantities like length, height, weight, density, etc, in a meaningful figure. These are further classified as,
1. Rational Number: These are the numbers which can be represented in the form of a/b, where a and b are integers and b is not equal to 0. Rational numbers are either terminating or recurring in nature.
2. Irrational Number: These are the numbers which cannot be expressed as a/b and where b is not equal 0. Irrational numbers are neither non-terminating or non-recurring in nature.
Terminating Numbers: Terminating numbers are those numbers which stop after the decimal point.
Non- Terminating Numbers: Non- terminating numbers are the numbers which don’t stop after the decimal numbers.
Recurring Numbers: The part of the number which keeps on recurring again-again is termed as a recurring number. Generally, non-terminating numbers are classified as recurring numbers.
Non-recurring Numbers: Non-recurring numbers are those numbers which don’t keep on recurring again and again.
Types of Numbers –
1. Natural Numbers: It is the set of positive numbers.
2. Whole numbers: It is the set of all natural numbers including 0.
3. Integers: Integers is the set of all whole numbers along with negative numbers.
4. Even Numbers: Set of numbers exactly divisible by 2.
5. Odd Numbers: Set of numbers not exactly divisible by 2.
Factors and Multiples
If a number x divides y perfectly, then x is considered as a factor of y and y becomes the multiple of x.
For example, 4 is a factor of 16, 18 is a multiple of 6.
Prime Numbers: Prime numbers are the numbers which have no factor other than 1 and itself.
Composite Numbers: Composite numbers are those numbers which have other factors besides 1 and itself i.e. it has more than 2 factors. Numbers which are not prime are called as composite numbers.
Note: Except 1 any natural number can be classified as a prime or composite number.
Fractions:
A fraction denotes a part or parts of a unit. It is majorly classified into following types-
1. Proper Fractions: In a proper fraction the numerator is always less than the denominator. Proper Fractions are always less than 1.
2. Improper Fraction: In an improper fraction the numerator is more than the denominator. Improper Fractions are greater than 1.
3. Mixed Fraction: A mixed fraction consists of two parts i.e. The fractions which consist of two parts i.e. the integer part and a fractional part. All mixed fractions are improper fractions.
Answer:
The method of representing and working with numbers is called number system. Every number system has some unique digits, which are vombined to form bigger numbers . The total number of unique digits in a number system is called its base or radix. There are four types of number systems :-
1.)Decimal number system
2.)Binary number system
3.)Octal number system
4.)Hexadecimal number system