## RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.4

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.4

**Other Exercises**

- RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.1
- RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.2
- RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.3
- RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.4
- RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.5
- RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.6
- RD Sharma Class 9 Solutions Chapter 1 Number Systems MCQS

**Question 1.**

**Define an irrational number.**

**Solution:**

A number which cannot be expressed in the form of where p and q are integers and q ≠ 0 is called an irrational number.

**Question 2.**

**Explain, how irrational numbers differ from rational numbers?**

**Solution:**

A rational number can be expressed in either terminating decimal or non-terminating recurring decimals but an irrational number is expressed in non-terminating non-recurring decimals.

**Question 3.**

**Examine, whether the following numbers are rational or irrational:**

**Solution:**

**Question 4.
**

**Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:**

**Solution:**

**Question 5.
**

**In the following equation, find which variables x, y, z etc. represent rational or irrational numbers:**

**Solution:**

**Question 6.
**

**Given two rational numbers lying between 0.232332333233332… and 0.212112111211112.**

**Solution:**

Two rational numbers lying between 0.232332333233332… and 0.212112111211112… will be 0.232 and 0.212

**Question 7.
**

**Give two rational numbers lying between 0.515115111511115… and 0.5353353335…**

**Solution:**

**Two rational numbers lying between 0.515115111511115… and 0.535335333533335… will be 0.515, 0.535**

**Question 8.
**

**Find one irrational numbers between 0.2101 and 0.2222… = 0..**

**Solution:**

One irrational number lying between 0.2101 and 0.2222… = 0. will be 2201.0010001…

**Question 9.
**

**Find a rational number and also an irrational number lying between the numbers, 0.3030030003… and 0.3010010001…**

**Solution:**

Between two numbers 0.3030030003… and 0.3010010001…, a rational will be 0.301 and irrational number will be 0.3020020002…

**Question 10.
**

**Find three different irrational numbers between the rational numbers and . [NCERT]**

**Solution:**

**Question 11.
**

**Give an example of each, of two irrational numbers whose:**

**(i) difference is a rational number.**

**(ii) difference is an irrational number.**

**(iii) sum is a rational number.**

**(iv) sum is an irrational number.**

**(v) product is a rational number.**

**(vi) product is an irrational number.**

**(vii) quotient is a rational number.**

**(viii) quotient is an irrational number.**

**Solution:**

**(i)**Two numbers whose difference is also a rational number, e.g.

, which are irrational numbers.

∴ Difference = – = 0 which is also a rational number.

**(ii)**Two numbers whose difference is an irrational number.

e.g. and which are irrational numbers.

Now difference = – which is also an irrational number.

**(iii)**Let two irrational numbers be and – which are irrational numbers.

Now sum = + (-) =

– = 0 Which is a rational number.

**(iv)**Let two numbers be , which are irrational numbers.

Now sum = + which is an irrational number.

**(v)**Let numbers be +and –which are irrational numbers.

Now product = ( + ) ( –)

= 3-2 = 1 which is a rational number.

**(vi)**Let numbers be and , which are irrational number.

Now product = x =

^{=}

which is an irrational number.

**(vii)**Let numbers be 6 and 2 which are irrational numbers.

Quotient = = 3 which is a rational number.

**(viii)**Let numbers be and which are irrational numbers.

Now quotient = = which is an irrational number.

**Question 12.
**

**Find two irrational numbers between 0.5 and 0.55.**

**Solution:**

Two irrational numbers between 0.5 and 0.55 will be 0.51010010001… and 52020020002…

**Question 13.
**

**Find two irrational numbers lying betwee 0.1 and 0.12.**

**Solution:**

Two irrational numbers lying between 0.1 and 0.12 will be 0.1010010001… and 0.1020020002…

**Question 14.
**

**Prove that + is an irrational number.**

**Solution:**

Hope given RD Sharma Class 9 Solutions Chapter 1 Number Systems Ex 1.4 are helpful to complete your math homework.

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