What is the difference between Rational and Irrational numbers? - Future Study Point

What is the difference between Rational and Irrational numbers?

difference between rational number and irrational number

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

Study all types of numbers

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

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

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Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
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Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
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Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

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NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
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