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# 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?
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

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

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

### 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