Important questions for Class 9 Maths Chapter 1 Number system are given here. These practice questions will help the students to build a better understanding of the Number system concept in Maths. These Class 9 Chapter 1 questions are important for CBSE Class 9 Maths exams. These important questions give an overview of the question types that are asked in the final exams and so students are able to face the exams more confidently.

## Number System Important Questions For Class 9 (Chapter 1)

Below given important Number system questions for 9th class students will help them to get acquainted with a wide variation of questions and thus, develop problem-solving skills.

**Q.1:** Find five rational numbers between 1 and 2.

**Solution:**

We have to find five rational numbers between 1 and 2.

So, let us write the numbers with denominator 5 + 1 = 6

Thus, 6/6 = 1, 12/6 = 2

From this, we can write the five rational numbers between 6/6 and 12/6 as:

7/6, 8/6, 9/6, 10/6, 11/6

**Q.2:** Find five rational numbers between 3/5 and 4/5.

**Solution:**

We have to find five rational numbers between 3/5 and 4/5.

So, let us write the given numbers by multiplying with 6/6, (here 6 = 5 + 1)

Now,

3/5 = (3/5) × (6/6) = 18/30

4/5 = (4/5) × (6/6) = 24/30

Thus, the required five rational numbers will be: 19/30, 20/30, 21/30, 22/30, 23/30

**Q.3:** Locate √3 on the number line.

**Solution:**

Construct BD of unit length perpendicular to OB (here, OA = AB = 1 unit) as shown in the figure.

By Pythagoras theorem,

OD = √(2 + 1) = √3

Taking O as the centre and OD as radius, draw an arc which intersects the number line at the point Q using a compass.

Therefore, Q corresponds to the value of √3 on the number line.

**Q.4:** Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

**Solution:**

No, since the square root of a positive integer 16 is equal to 4. Here, 4 is a rational number.

**Q.5: **Find the decimal expansions of 10/3, 7/8 and 1/7.

**Solution:**

Therefore, 10/3 = 3.3333…

7/8 = 0.875

1/7 = 0.1428571…Q.6:Show that 0.3333…=0.3¯ can be expressed in the form p/q, where p and q are integers and q≠0.

**Solution:**

Let x = 0.3333….

Multiply with 10,

10x = 3.3333…

Now, 3.3333… = 3 + x (as we assumed x = 0.3333…)

Thus, 10x = 3 + x

10x – x = 3

9x = 3

x = 1/3

Therefore, 0.3333… = 1/3. Here, 1/3 is in the form of p/q and q ≠ 0.

**Q.7:** What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

**Solution:**

Thus, 1/17 = 0.0588235294117647….

Therefore, 1/17 has 16 digits in the repeating block of digits in the decimal expansion.

**Q.8:** Find three different irrational numbers between the rational numbers 5/7 and 9/11.

**Solution:**

The given two rational numbers are 5/7 and 9/11.

5/7 = 0.714285714…..

9/11 = 0.81818181……

Hence, the three irrational numbers between 5/7 and 9/11 can be:

0.720720072000…

0.730730073000…

0.808008000…

**Q.9:** Visualise 3.765 on the number line, using successive magnification.

**Solution:**

Visualisation of 3.765 on the number line, using successive magnification is given below:

**Q.10: **Add 2√2+ 5√3 and √2 – 3√3.

**Solution:**

(2√2 + 5√3) + (√2 – 3√3)

= 2√2 + 5√3 + √2 – 3√3

= (2 + 1)√2 + (5 – 3)√3

= 3√2 + 2√3

**Q.11:** Simplify: (√3+√7) (√3-√7).

**Solution:**

(√3 + √7)(√3 – √7)

Using the identity (a + b)(a – b) = a^{2} – b^{2},

(√3 + √7)(√3 – √7) = (√3)^{2} – (√7)^{2}

= 3 – 7

= -4

**Q.12:** Rationalise the denominator of 1/[7+3√3].

**Solution:**

1/(7 + 3√3)

By rationalizing the denominator,

= [1/(7 + 3√3)] [(7 – 3√3)/(7 – 3√3)]

= (7 – 3√3)/[(7)^{2} – (3√3)^{2}]

= (7 – 3√3)/(49 – 27)

= (7 – 3√3)/22

**Q.13:** Represent √(9.3) on the number line.

**Solution:**

Representation of √9.3 on the number line is given below:

**Q.14:** Simplify:

(i) 7^{2/3}.7^{1/5}

(ii) 10^{1/2}/10^{1/4}

Solution:

(i) 7^{2/3}.7^{1/5}

Bases are equal, so add the powers.

7^{(2/3 + 1/5)}

= 7^{(10 + 3)/15}

= 7^{13/15}

(ii) 10^{1/2}/10^{1/4}

Bases are equal, so subtract the powers.

= 10 ^{(1/2 – 1/4)}

= 10^{1/4}

**Q.15:** What is the product of a rational and an irrational number?

a) Always an integer

b) Always a rational number

c) Always an irrational number

d) Sometimes rational and sometimes irrational

**Correct answer:** Option (c)

Explanation:

The product of a rational and an irrational number is always an irrational number.

For example, 2 is a rational number and √3 is irrational. Thus, 2√3 is always an irrational number.

**Q.16: **What is the value of (256)^{0.16} X (256)^{0.09}?

a) 4

b) 16

c) 64

d) 256.25

**Correct answer:** Option (a)

(256)^{0.16} x (256)^{0.09} = (256)^{(0.16 + 0.09)}

= (256)^{0.25}

= (256)^{(25/100)}

= (256)^{(1/4)}

= (4^{4})^{(1/4)}

= 4^{4(1/4)}

= 4