Numbers are used in various arithmetic operations as addition, subtraction, multiplication, etc which are applicable in daily businesses and trading activities. Numerals or numbers are the mathematical values used for, counting, measurements, labeling or recognizing time, and for many other activities. Numbers are generally also known as numerals.
The number system includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures as well as words accordingly. For example, The numbers like 40 and 65 expressed in the form of figures can also be written as forty and sixty-five.
Numbers are the mathematical or arithmetic figures used for the purpose of counting, measuring, and other arithmetic calculations. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.
A Number system or numeral system is defined as a standardized system to express numbers. It is the3 unique way of representation in which numbers are represented in arithmetic and algebraic structure.
The value of a number is determined by:
- The digit
- Its place value in the number
- The base of the number system
Types Of Numbers
There are different types of numbers categorized into sets by the number system. The types are described below:
- Natural numbers: Natural numbers are the positive numbers that count from 1 to infinity. The set of natural numbers is represented by ‘N’. It is the numbers we generally use for counting. The set of natural numbers can be represented as N=1,2,3,4,5,6,7,……………
- Whole numbers: Whole numbers are positive numbers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is represented by ‘W’. The set can be represented as W=0,1,2,3,4,5,………………
- Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by ‘Z. The set of integers can be represented as Z=………..,-5.-4,-3,-2,-1,0,1,2,3,4,5,………….
- Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can be expressed as 2.5,0.567, etc.
- Real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R”.
- Complex number: Complex numbers are a set of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
- Rational numbers: Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’.
- Irrational numbers: Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’.
What are Rational Numbers?
The numbers which can be expressed as fractions or ratio of two integers and also can be written as a positive number, negative number, prime, and even zero is called rational numbers.
It can be expressed as p/q, where q ≠ 0
For example, 2/3 is a rational number that expresses that 2 integers are divided by 3 integers.
What are Irrational Numbers?
Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. it can be written in decimals and have endless non-repeating digits after the decimal point.
For example 2.65432……..
What are the rational numbers between 3 and 5?
The rational numbers between 3 and 5 are 31/10, 32/10, 33/10, 34/10, 35/10, 36/10,………….., 49/10.
To find out a set of rational numbers between two numbers suppose A and B we need to express numbers A and B in rational numbers.
Let’s express 3 and 5 as rational numbers as
⇒3 = 3 × 10/10 =30/40
⇒5 = 5 × 10/10 =50/10
Hence, the rational numbers between 3 and 5 are 30/10, and 50/10 are 31/10, 32/10, 33/10, 34/10, 35/10, 36/10, 37/10, 38/10, 39/10, 40/10, ………….., 49/10.
Question 1: What are the five rational numbers between 0 and 1?
The rational numbers between 0 and 1 are 12, 21, 34, 41, and 51.
Question 2: How can we express rational numbers?
We can express a rational number as p/q, where, q is a non-zero denominator.
Whether you're preparing for your first job interview or aiming to upskill in this ever-evolving tech landscape, GeeksforGeeks Courses
are your key to success. We provide top-quality content at affordable prices, all geared towards accelerating your growth in a time-bound manner. Join the millions we've already empowered, and we're here to do the same for you. Don't miss out - check it out now!