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What is the difference between Rational and Irrational numbers?

difference between rational number and irrational number

Rational numbers are the numbers that are written in the form of p/q, where p and q are the integer co-prime numbers and Irrational numbers are the numbers that can not be written in the form of p /q. All types of numbers, natural numbers, whole numbers, and integers are Rational numbers, and all unresolved roots,π,e, etc are Irrational numbers.

Natural Numbers: All those numbers which are used to count things are known as Natural numbers, the set of natural numbers is {1,2,3,4,5,6……….}. Natural numbers are Rational Numbers because we can write them in the form of P/Q

Whole Numbers: All those numbers which are complete numbers are known as Whole numbers, the set of Whole numbers is {0,1,2,3,4,5,6……….} . Whole numbers are Rational Numbers because we can write them in the form of P/Q

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What is the difference between Rational and Irrational numbers?

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Integers: Integers is the set of all the complete numbers in minus and positive including 0 also. If surface of the earth is 0 then height above the ground is shown by positive integers and depth below the surface of the earth is shown by negative integers.

All the integers are rational numbers because we can write them in the form of p/q, as example.

All the fractions that exist between the integers are also rational numbers. There are two types of fractional numbers on the basis of decimal expansion.

Type of rational number on the basis of decimal expansion:

On the basis of the decimal expansion, the rational numbers are of two kinds

(a) Finite Decimal (b) Infinite Decimal

 Finite Decimal: The fraction p/q (p and q are co-prime no’s) when converted into decimal expansion, we get a quotient and remainder 0.as an example

These types of decimal expansion are known as finite decimals. We can observe a fraction p/q (p and q are co-prime no’s) to be a finite decimal if factors of q are in the form of 2n× 5n. So, if there is any other prime factor except to 2 and 5 of q then the decimal expansion of p/q can’t be finite decimal.

 Infinite Decimal: The fraction p/q(p and q are co-prime no’s) when converted into decimal expansion,we get a quotient and remainder  non-zero.as an example

We can observe a fraction p/q (p and q are co-prime no’s) to be an infinite decimal if factors of q are not in the form of 2n× 5n. So, if there is any other prime factor except 2 and 5 of q then the decimal expansion of p/q is infinite decimal.

Irrational number: All the infinite decimals that are non-recurrent decimals are known as irrational numbers. As an example, the decimal expansions of√2,√3,√5 , and π are infinite non-recurrent decimal expansions so these are irrational numbers. The decimal expansion such as 2.804005606006….are known as irrational numbers since after the decimal the numbers are not repeated.

√2 = 1.41421356…..,√6= 2.4494897…….

What is the difference between rational and irrational number?

The features of rational numbers and irrational numbers are following.

  • The sum of two irrational numbers may be an irrational number or a rational number, as an example (√2+ 4), (π + 2) are irrational numbers and √2 + (-√2) = 0
  • The product of an irrational number to a rational number is an irrational number, as an example, 2√5,2π are irrational number.
  • The product of two irrational number may be a rational or irrational number, as an example √2×–√2=-2,√2×√3 = √6
  • The product of two identical irrational numbers may be rational or irrational, as an example √2×√2 = 2,
  • The division of two irrational numbers can be rational or irrational, as an example 2√2/3√2= 2/3 , 2√2/√3 etc.

What is the difference between rational and irrational number?

Is π an irrational number, what are rational, irrational, and surds numbers?

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π is written in the form of 22/7 then why is it an irrational number:π is the ratio between circumference and diameter, one of them either circumference or diameter is an irrational number, so π is called an irrational number, the value 22/7 of π we use in the calculation is actually the nearest rational value of π, therefore 22/7 is a rational number but π is an irrational number.

Questions related to Rational numbers and Irrational numbers

Click here to get the answers to the following questions: Number System (all types of numbers used in maths)

Q1.Find whether the following are finite decimal or infinite decimal

Q2.Write the following rational number in ascending form

Q3. Write the following irrational number in acending number

Click here:What are Surds and how to compare them?

Q4.Write the following infinite recurrent decimal number into the form of p/q.

Q5. Rationalize the denominator of the following fractions

Q6. Find the value of a and b

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NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial Chapter 10-Circles
Chapter 3- Coordinate Geometry Chapter 11-Construction
Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles Chapter 14-Statistics
Chapter 7-Triangles Chapter 15-Probability
Chapter 8- Quadrilateral

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Chapter 1-Matter in our surroundings Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure? Chapter 10- Gravitation
Chapter3- Atoms and Molecules Chapter 11- Work and Energy
Chapter 4-Structure of the Atom Chapter 12- Sound
Chapter 5-Fundamental unit of life Chapter 13-Why do we fall ill ?
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Chapter 7- Diversity in living organism Chapter 15-Improvement in food resources
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Chapter 1-Real number Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial Chapter 10-Circles
Chapter 3-Linear equations Chapter 11- Construction
Chapter 4- Quadratic equations Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression Chapter 13-Surface areas and Volume
Chapter 6-Triangle Chapter 14-Statistics
Chapter 7- Co-ordinate geometry Chapter 15-Probability
Chapter 8-Trigonometry

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Chapter 1- Chemical reactions and equations Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds Chapter 12- Electricity
Chapter 5-Periodic classification of elements Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process Chapter 14-Sources of Energy
Chapter 7-Control and Coordination Chapter 15-Environment
Chapter 8- How do organisms reproduce? Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-Sets Chapter 9-Sequences and Series
Chapter 2- Relations and functions Chapter 10- Straight Lines
Chapter 3- Trigonometry Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations Chapter 15- Statistics
Chapter 8- Binomial Theorem  Chapter 16- Probability

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NCERT solutions for class 12 maths

Chapter 1-Relations and Functions Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra
Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability Chapter 13-Probability
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