Rational Numbers: NCERT Class 9 Maths

Let’s dive into fundamental concept of rational numbers from NCERT Class 9 Maths Chapter 1, which forms a cornerstone of our number system.

What are Rational Numbers?

A rational number is any number that can be written as a fraction p/q, where p and q are integers and q is not zero.

In simpler terms: if you can express a number as one integer divided by another (non-zero) integer, then it’s rational.

NCERT Class 9 Maths introduces rational numbers as one of the first concepts because they’re essential for understanding more complex mathematical ideas later in the curriculum.

Rational numbers include:

All integers (like -3, -2, -1, 0, 1, 2, 3…)
All fractions (like 1/2, 3/4, 5/7…)
Terminating decimals (like 0.75, 2.5…)
Repeating decimals (like 0.333… or 0.142857142857…)

Is 0 a Rational Number?

Yes, zero is indeed a rational number. Why? Because we can write it as 0/1, fitting our definition perfectly. Zero is the numerator, and 1 is the denominator.

In fact, we can represent zero as 0/n for any non-zero integer n (like 0/5, 0/100, etc.). All these representations equal the same value: zero.

Is Pi a Rational Number?

No, π (pi) is not a rational number. It cannot be expressed as a fraction p/q where p and q are integers. The decimal expansion of π (3.14159265359…) never terminates and never repeats in a pattern. This makes π an irrational number.

NCERT Class 9 Maths explains that irrational numbers like π and √2 have non-terminating, non-recurring decimal expansions, distinguishing them from rational numbers.

NCERT Solutions Class 9 Maths for Exercise 1.1

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

Answer: Yes, zero is a rational number. It can be written as 0/1, where p = 0 and q = 1. Here, both p and q are integers, and q ≠ 0.

Question 2: Find six rational numbers between 3 and 4.

Answer: We can find these numbers using several methods:

Method 1: Convert to equivalent fractions with denominator 7

3 = 21/7 and 4 = 28/7
So, 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7 are six rational numbers between 3 and 4.

Method 2: Use decimal representation

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

Question 3: Find five rational numbers between 3/5 and 4/5.

Answer: To find rational numbers between 3/5 and 4/5, we can convert to equivalent fractions with a larger denominator:

3/5 = 12/20 and 4/5 = 16/20
Numbers between them are 13/20, 14/20, 15/20, 13.5/20, and 14.5/20

Question 4: State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.

Answer: True. Natural numbers are counting numbers (1, 2, 3…), and whole numbers include all natural numbers plus zero. So every natural number belongs to the set of whole numbers.

(ii) Every integer is a whole number.

Answer: False. Integers include negative numbers (…-3, -2, -1), zero, and positive numbers (1, 2, 3…). Whole numbers include only zero and positive integers. Negative integers are not whole numbers.

(iii) Every rational number is a whole number.

Answer: False. Rational numbers include fractions like 1/2, 2/3, etc., which are not whole numbers. While every whole number is rational (can be written as n/1), not every rational number is a whole number.

Understanding Decimal Forms of Rational Numbers

The NCERT Class 9 Maths textbook emphasizes that every rational number has either a terminating decimal expansion or a non-terminating recurring decimal expansion.

For example:

1/4 = 0.25 (terminating)
1/3 = 0.333… (non-terminating recurring)
7/8 = 0.875 (terminating)

This special property helps us identify rational numbers in decimal form. If a decimal either terminates or has a pattern that repeats forever, it’s rational.

By mastering rational numbers as presented in NCERT Solutions Class 9 Maths Chapter 1, you’ve taken a big step in understanding the building blocks of mathematics. These concepts will help you tackle more complex topics with confidence in your further studies.

See more:

Read about Irrational Numbers: Class 9 Maths

Click here to explore more Number Systems: Chapter 1- NCERT Maths Class 9