# What is the difference between Rational and Irrational numbers?

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

**What are Surds and how to compare them?**

**Number System (all types of numbers used in maths)**

**How to creat and solve algebraic equations like linear and quadratic equations**

**Three ways of solving quadratic equations**

**Achieve hundred percentage marks in maths**

**Solutions of the questions based on expression and equations**

**Tips of developing memory power and qualifying a government entrance exams**

**Tips to get success in competitive exams**

**Finding the roots of the polynomial by the complete square method**

**Three Ways of Solving Quadratic Equations**

**Addition, subtraction, multiplication and division of polynomials**

# What is the difference between Rational and Irrational numbers?

Click for online shopping

**Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc**

**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 2^{n}× 5^{n}. 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 2^{n}× 5^{n}. 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?**

**See the video**

**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**

**NCERT Solutions for class 9 science **

**NCERT Solutions for class 10 maths**

**CBSE Class 10-Question paper of maths 2021 with solutions**

**CBSE Class 10-Half yearly question paper of maths 2020 with solutions**

**CBSE Class 10 -Question paper of maths 2020 with solutions**

**CBSE Class 10-Question paper of maths 2019 with solutions**

**NCERT Solutions for Class 10 Science**

**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 |

**CBSE Class 11-Question paper of maths 2015**

**CBSE Class 11 – Second unit test of maths 2021 with solutions**

**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 |

Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |

Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

**Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2**

**Class 12 Maths Important Questions-Application of Integrals**

**Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22**

**Solutions of class 12 maths question paper 2021 preboard exam CBSE Solution**

You can compensate us

**Paytm number 9891436286**

The money collected by us will be used for the education of poor students who leaves their study because of a lack of money.