Recurrent and Non -Recurrent Decimal Numbers

 

Recurrent and Non-Recurrent Decimal Numbers: Before knowing what are Recurrent and Non -Recurrent Decimal Numbers it is important for us to understand the types of decimal numbers, decimal numbers are of two kinds, finite decimal and infinite decimal, as example finite decimal is the outcome of 1/2=0.5, it is finite because after dividing 1 by 2, the remainder comes 0, taking another example 1/3=0.33333…., in this case, the remainder never comes 0 and as a result after the decimal 3 is repeating continually so such decimal numbers are called Infinite recurring decimal numbers, taking third example √2=1.41421356237……., this is also an infinite decimal number but after decimal the numbers are not repeating, such decimal numbers are known as non-recurrent infinite decimal numbers.

Questions based on Recurrent and Non-recurrent decimal numbers:

Question1:Are all infinite decimal numbers are Rational numbers?

Answers: No,The numbers which are written in the form of P/Q are known as rational numbers.The numbers 1/2=0.5 and 1/3=0.333—-,so both decimal numbers finite and infinite recurrent decimal numbers can be written in the form of P/Q, so these decimal numbers are k are rational numbers.

Question 2:What are non-recurrent infinite decimal numbers called?

Non-recurrent infinite decimal numbers are called irrational numbers as example √2,√3,π.
The decimal expansion of √2,√3,π
√3=1.73205080757……
π=3.14159…….

The decimal expansion of all unresolved roots(√2,√3 etc) is always a non-recurring decimal and the numbers like π,e is also non-recurring decimal, so all non-recurrent infinite decimals are known as irrational numbers.

Question 3:π is written 22/7, then why is it called an irrational number?

Answers:π is the ratio between circumference and diameter, practically its value is evaluated by many mathematicians which comes to π=3.14159265358979…….,it can be assumed that either circumference or diameter or both can be irrational. The value of π=3.14 or 22/7 is actually an approximate value that we use in mathematics, and of course, this value 3.14 or 22/7 is a rational number.So the extraction is π is an irrational number but 3.14 or 22/7 is rational number.

Q4:How can you write 3.121212…in the form of P/Q?
Answer:
step 1:Write the given number equivalent to a variable
x = 3.121212…..(i)
step 2:Since after decimal two digits are repeating,so place two zeroes after 1 that makes 100,multiply equation (1) by 100
100x =312.121212…..(ii)
Subtract equation (i) from equation (ii),we get
99x =308
x =308/99
Therefore
3.121212…=308/99

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

NCERT Solutions of 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

NCERT Solutions of class 9 science 

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 ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

NCERT Solutions of class 10 maths

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

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 of class 10 science

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

Solutions of class 10 last years Science question papers

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -Latest sample paper of science

NCERT solutions of 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 of 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