# NCERT Solutions for Class 9 Maths Chapter 1

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems in Hindi Medium and English medium PDF form to free download. Solutions are updated according to Latest CBSE Syllabus 2019-20 for the students of CBSE Board as well as UP Board following NCERT Books for their final exam March 2020.

 Class 9: Maths – गणित Chapter 1: Number Systems ## NCERT Solutions for Class 9 Maths Chapter 1

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### Class 9 Maths Chapter 1 Number Systems

#### Solutions in Hindi Medium and English Medium

• Class 9 Maths Chapter 1 Exercise 1.1 Solutions
• Class 9 Maths Chapter 1 Exercise 1.2 Solutions
• Class 9 Maths Chapter 1 Exercise 1.3 Solutions

• Natural numbers are those numbers which are used for counting.
• Whole numbers are the collection of all natural numbers together with zero.
• Integers are the collection of all whole numbers and negative of natural numbers.
• Rational numbers are those numbers which can be expressed in the form of p/q, where p, q are integers and q is not equal to 0.
• Irrational numbers are those numbers which cannot be expressed in the form of p/q, where p, q are integers and q is not = 0.
• Real numbers are the collection of all rational and irrational numbers.

• Two numbers are said to be equivalent, if numerators and denominators of both are in proportion or they are reducible to be equal.
• The decimal expansion of real numbers can be terminating or non-terminating repeating or non-terminating non-repeating.
• The decimal expansion of rational numbers can either be terminating or non-terminating and vice-versa.
• The decimal expansion of irrational numbers can either be non-recurring and vice-versa.

• If ‘a’ is a rational and ‘b’ is an irrational, then a + b and a – b are irrational, and ab and a/b are irrational numbers, where b is not equal to 0.
• If ‘a’ and ‘b’ both are irrational, then a+b, a-b, ab and a/b may be rational or irrational.
• If ‘a’ be any real number and ‘n’ be any positive integer such that a^1/n = n√a is a real number, then ‘n’ is called exponent, ‘a’ is called radical and ‘√’ is called radical sign.

#### Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q≠0?

Yes, zero is a rational number.
It can be written in the form of p/q. For example: 0/1, 0/2, 0/5 are rational numbers, where p and q are integers and q≠0.

#### कथन सत्य हैं या असत्य? कारण के साथ अपने उत्तर दीजिए। प्रत्येक अपरिमेय संख्या एक वास्तविक संख्या होती है।

सत्य, क्योंकि सभी परिमेय और अपरिमेय संख्याओं का संग्रह ही वास्तविक संख्या होती है।

#### क्या सभी धनात्मक पूर्णांकों के वर्गमूल अपरिमेय होते हैं? यदि नहीं, तो एक ऐसी संख्या के वर्गमूल का उदाहरण दीजिए जो एक परिमेय संख्या है।

सभी धनात्मक पूर्णांकों के वर्गमूल अपरिमेय नहीं होते हैं। जैसे कि √4 = 2, जो एक परिमेय संख्या है।

#### Simplify each of the following expression: (3 + √3)(2 + √2)

(3 + √3)(2 + √2)
= 6 + 3√2 + 2√3 + √6

#### Find six rational numbers between 3 and 4.

Six rational numbers between 3 and 4 are 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

#### Express 0.99999… in the form of p/q . Are you surprised by your answer?

0.99999…
Let x = 0.99999… … (i)
Multiplying equation (i) by 10 both sides
10x = 9.99999…
⇒ 10x = 9 + 0.99999……
⇒ 10x = 9 + x [From equation (i)] ⇒ 10x – x = 9
⇒ 9x = 9
⇒ x = 9/9 = 1
The answer makes sense as 0.99999… is very close to 1, that is why we can say that 0.99999=1.

#### Write three numbers whose decimal expansions are non-terminating non-recurring.

Three non-terminating non-recurring decimals:
0.414114111411114…
2.01001000100001…
π=3.1416…

9^(3/2)
= (3^2 )^(3/2)
= 3^(2×3/2)
= 3^3
= 27

## 4 thoughts on “NCERT Solutions for Class 9 Maths Chapter 1”

1. Rajeev says:

Thank you sir yah website very good he

2. Manoj mishr says:

More about question ka solutions chahiye
जो कि तिवारी वेबसाइट के सबसे निचले पेज पर दिया है

3. ranga sai says:

sai ram and thank you so much it really helped me a lot

4. Devdasji says:

thank you so much sir . easy to understand . very interesting