## RD Sharma Class 9 Solutions Chapter 1 Number Systems MCQS

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

**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

**the correct alternative in each of the following:**

**Question 1.
**

**Which one of the following is a correct statement?**

**(a) Decimal expansion of a rational number is terminating**

**(b) Decimal expansion of a rational number is non-terminating**

**(c) Decimal expansion of an irrational number is terminating**

**(d) Decimal expansion of an irrational number is non-terminating and non-repeating**

**Solution:**

Decimal expansion of an irrational number is non-terminating and non-repeating .

**(d)**

**Question 2.
**

**Which one of the following statements is true?**

**(a) The sum of two irrational numbers is always an irrational-number**

**(b) The sum of two irrational numbers is always a rational number**

**(c) The sum of two irrational numbers may be a rational number or an irrational number**

**(d) The sum of two irrational numbers is always an integer**

**Solution:**

The sum of two irrational numbers may be a rational number or an irrational number

**(c)**

**Question 3.
**

**Which of the following is a correct statement?**

**(a) Sum of two irrational numbers is always irrational**

**(b) Sum of a rational and irrational number is always an irrational number**

**(c) Square of an irrational number is always a rational number**

**(d) Sum of two rational numbers can never be an integer**

**Solution:**

Sum of a rational and irrational number is always an irrational number

**(b)**

**Question 4.
**

**Which of the following statements is true?**

**(a) Product of two irrational numbers is always irrational**

**(b) Product of a rational and an irrational number is always irrational**

**(c) Sum of two irrational numbers can never be irrational**

**(d) Sum of an integer and a rational number can never be an integer**

**Solution:**

Product of a rational and an irrational number is always irrational

**(b)**

**Question 5.
**

**Which of the following is irrational?**

**Solution:**

**Question 6.**

**Which of the following is irrational?**

**(a) 14 **

**(b) 0.14\(\overline { 16 }\) **

**(c) 0.\(\overline { 1416 }\) **

**(d) 0.1014001400014
**

**Solution:**

0.1014001400014…….. is irrational as it is non-terminating nor repeating decimal,

**(d)**

**Question 7.
**

**Which of the following is rational?**

**Solution:**

**Question 8.
**

**The number 0.318564318564318564… is:**

**(a) a natural number**

**(b) an integer**

**(c) a rational number**

**(d) an irrational number**

**Solution:**

The number = 0.318564318564318564…………

= 0.\(\overline { 318564 }\)

**∵ The decimal is non-terminating and recurring**

∴ It is rational number.

**(c)**

**Question 9.
**

**If n is a natural number, then \(\sqrt { n } \)is**

**(a) always a natural number**

**(b) always a rational number**

**(c) always an irrational number**

**(d) sometimes a natural number and sometimes an irrational number**

**Solution:**

If n is a natural number then \(\sqrt { n } \) may sometimes a natural number and sometime an irrational number e.g.

If n = 2 then \(\sqrt { n } \) =\(\sqrt { 2 } \) which is are irrational and if n = 4, then \(\sqrt { n } \)= \(\sqrt { 4 } \) = 2 which is a rational number.

**(d)**

**Question 10.
**

**Which of the following numbers can be represented as non-terminating, repeating decimals?**

**Solution:**

**Question 11.
**

**Every point on a number line represents**

**(a) a unique real number**

**(b) a natural number**

**(c) a rational number**

**(d) an irrational number**

**Solution:**

Every point on a number line represents a unique real number.

**(a)**

**Question 12.
**

**Which of the following is irrational?**

**(a) 0.15**

**(b) 0.01516**

**(c) 0.\(\overline { 1516 }\)**

**(d) 0.5015001500015..**

**Solution:**

As it is non-terminating non-repeating decimals while others are terminating or non-terminating repeating decimals.

**(d)**

**Question 13.
**

**The number 1.\(\overline { 27 }\) in the form \(\frac { p }{ q }\) , where p and q are integers and q ≠ 0, is**

**Solution:**

**Question 14.**

**Solution:**

**Question 15.**

**Solution:**

**Question 16.**

**Solution:**

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

**Question 19.**

**Solution:
**An irrational number between 2 and 2.5 is \(\sqrt { 5 } \) as it has approximate value 2.236…

**(b)**

**Question 20.
**

**The number of consecutive zeros in 2**

^{3}x 3^{4 }x 5^{4}x 7, is**(a) 3**

**(b) 2**

**(c) 4**

**(d) 5**

**Solution:**

In 2

^{3}x 3

^{4}x 5

^{4}x 7, number of consecutive zero will be 3 as 2

^{3}x 5

^{4}= 2 x 2 x 2 x 5x 5 x 5 x 5 = 5000

**(a)**

**Question 21.
**

**The smallest rational number by which \(\frac { 1 }{ 3 }\) should be multiplied so that its decimal expansion terminates after one place of decimal, is**

**Solution:**

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

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