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## NCERT Class 9 Maths Textbook Chapter 1 With Answer Book PDF Free Download

### Chapter 1: Number Systems

#### 1.1 Introduction

In your earlier classes, you have learned about the number line and how to represent various types of numbers on it

#### 1.2 Irrational Numbers

We saw, in the previous section, that there may be numbers on the number line that are not rational.

In this section, we are going to investigate these numbers. So far, all the numbers you have come across, are of the form p/q, where p and q are integers and q ≠ 0. So, you may ask: are there numbers that are not of this form? There are indeed such numbers.

#### 1.3 Real Numbers and Their Decimal Expansions

In this section, we are going to study rational and irrational numbers from a different points of view. We will look at the decimal expansions of real numbers and see if we can use the expansions to distinguish between rationals and irrational.

We will also explain how to visualize the representation of real numbers on the number line using their decimal expansions. Since rationals are more familiar to us, let us start with them.

Author | NCERT |

Language | English |

No. of Pages | 27 |

PDF Size | 785 KB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 9 Maths Chapter 1 Number Systems

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

Solution:

We know that a number is said to be rational if it can be written in the form p/q, where p and q are integers and q ≠ 0.

Taking the case of ‘0’,

Zero can be written in the form 0/1, 0/2, 0/3 … as well as, 0/1, 0/2, 0/3.

Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be a positive or negative number.

Hence, 0 is a rational number.

**2. Find six rational numbers between 3 and 4.**

Solution:

There are infinite rational numbers between 3 and 4.

As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6+1 = 7 (or any number greater than 6)

i.e., 3 × (7/7) = 21/7

and, 4 × (7/7) = 28/7. The numbers between 21/7 and 28/7 will be rational and will fall between 3 and 4.

Hence, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are the 6 rational numbers between 3 and 4.

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

Solution:

There are infinite rational numbers between 3/5 and 4/5.

To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers 3/5 and 4/5

with 5+1=6 (or any number greater than 5)

i.e., (3/5) × (6/6) = 18/30

and, (4/5) × (6/6) = 24/30

The numbers between18/30 and 24/30 will be rational and will fall between 3/5 and 4/5.

Hence,19/30, 20/30, 21/30, 22/30, 23/30 are the 5 rational numbers between 3/5 and 4/5

NCERT Class 9 Maths Textbook Chapter 1 With Answer Book PDF Free Download