Recurrent and Non -Recurrent Decimal Numbers - Future Study Point

Recurrent and Non -Recurrent Decimal Numbers

Recurrent and Non -Recurrent Decimal Numbers

Recurrent and Non -Recurrent Decimal Numbers

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

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?
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

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

NCERT Solutions of 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

NCERT Solutions of class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast 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 numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 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 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

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-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

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 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
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals




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