   Question Answers

# Give two rational numbers lying between 0.232332333233332….. and 0.212112111211112…..Enter 1 if the answer is 0.221, 0.222 otherwise enter 0.  Hint: In this particular question use the concept that rational number are terminating and recurring decimals whereas irrational numbers are non-terminating and non-recurring decimals and between two numbers there are infinitely many numbers are possible so use these concepts to reach the solution of the question.

Given numbers
0.232332333233332….. and 0.212112111211112…..
As we all know that irrational numbers are non – terminating and non – recurring decimals i.e. it cannot written in the form of $\dfrac{p}{q}$, where $q \ne 0$and p and q has not any common factors except 1.
So the given numbers are irrational numbers so it cannot be written in the form of $\dfrac{p}{q}$, where $q \ne 0$.
Now we have to find out the two rational numbers between the given numbers.
As we all know between these two irrational numbers there are infinitely many numbers possible some are rational numbers and some are irrational numbers.
So 0.221 and 0.222 is greater than 0.212112111211112…. and less than 0.232332333233332…. so rational numbers 0.221 and 0.222 are lying between them as shown in the below number line. Hence 0.221 and 0.222 are lying between the given irrational numbers.
So according to the question we have to enter 1.

Note: Whenever we face such types of questions the key concept we have to remember is that always recall that the rational numbers are written in the form of $\dfrac{p}{q}$, where $q \ne 0$ and irrational numbers cannot written in the form of $\dfrac{p}{q}$, where $q \ne 0$, where p and q has not any common factors except 1.

View Notes
CBSE Class 7 Maths Chapter 9 - Rational Numbers Formulas  CBSE Class 8 Maths Chapter 1 - Rational Numbers Formulas  Perfect Numbers  Prime Numbers  Cardinal Numbers  Co-Prime Numbers  Properties of Whole Numbers  CBSE Class 6 Maths Chapter 2 - Whole Numbers Formulas  CBSE Class 10 Maths Chapter 1 - Real Numbers Formula  CBSE Class 6 Maths Chapter 3 - Playing with Numbers Formulas  Important Questions for CBSE Class 7 Maths Chapter 9 - Rational Numbers  Important Questions for CBSE Class 8 Maths Chapter 1 - Rational Numbers  Important Questions for CBSE Class 9 Maths Chapter 4 - Linear Equations in Two Variables  Important Questions for CBSE Class 10 Maths Chapter 1 - Real Numbers  Important Questions for CBSE Class 6 Maths Chapter 2 - Whole Numbers  Important Questions for CBSE Class 8 Maths Chapter 16 - Playing with Numbers  Important Questions for CBSE Class 6 Maths Chapter 1 - Knowing Our Numbers  Important Questions for CBSE Class 9 Maths Chapter 9 - Areas of Parallelograms and Triangles  Important Questions for CBSE Class 6 Maths Chapter 3 - Playing with Numbers  NCERT Books for Class 9 Maths Chapter 9  CBSE Class 12 Maths Question Paper 2020  CBSE Class 10 Maths Question Paper 2020  Maths Question Paper for CBSE Class 10 - 2011  Maths Question Paper for CBSE Class 10 - 2008  CBSE Class 10 Maths Question Paper 2017  Maths Question Paper for CBSE Class 10 - 2012  Maths Question Paper for CBSE Class 10 - 2009  Maths Question Paper for CBSE Class 10 - 2010  Maths Question Paper for CBSE Class 10 - 2007  Maths Question Paper for CBSE Class 12 - 2013  NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers  NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers  NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers In Hindi  NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers (EX 9.1) Exercise 9.1  NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers (EX 9.2) Exercise 9.2  RS Aggarwal Class 8 Mathematics Solutions for Chapter-1 Rational Numbers  RD Sharma Class 8 Maths Solutions Chapter 1 - Rational Numbers  RD Sharma Class 7 Maths Solutions Chapter 4 - Rational Numbers  RD Sharma Solutions for Class 9 Maths Chapter 2 - Exponents of Real Numbers  RS Aggarwal Class 7 Solutions Chapter-4 Rational Numbers  