NCERT Class 9 Mathematics Exercise 1.1 Solutions – Number System

 solutions for NCERT Class 9 Mathematics - Chapter 1 (Number Systems), Exercise 1.1, in a unique and easy-to-understand manner:

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Exercise 1.1 Solutions – Number Systems

Q1. Is zero a rational number? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$?

Solution:

Yes, zero is a rational number because it can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$.

Example:

$$0 = \frac{0}{1}, \quad 0 = \frac{0}{2}, \quad 0 = \frac{0}{-3}, \quad 0 = \frac{0}{100}$$

Since 0 can be written as the ratio of two integers with a non-zero denominator, it is rational.

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Q2. Find six rational numbers between 3 and 4.

Solution:

To find six rational numbers between 3 and 4, we take the simplest approach:
We express 3 and 4 with a common denominator:

$$3 = \frac{30}{10}, \quad 4 = \frac{40}{10}$$

Now, we choose six numbers between 30/10 and 40/10:

$$\frac{31}{10}, \quad \frac{32}{10}, \quad \frac{33}{10}, \quad \frac{34}{10}, \quad \frac{35}{10}, \quad \frac{36}{10}$$

Thus, six rational numbers between 3 and 4 are:

$$3.1, 3.2, 3.3, 3.4, 3.5, 3.6$$

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Q3. Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.

Solution:

Since both fractions have the same denominator, we can find five numbers between them by increasing the numerator:

$$\frac{3}{5} = \frac{30}{50}, \quad \frac{4}{5} = \frac{40}{50}$$

Now, selecting five numbers between 30/50 and 40/50:

$$\frac{31}{50}, \quad \frac{32}{50}, \quad \frac{33}{50}, \quad \frac{34}{50}, \quad \frac{35}{50}$$

Thus, five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are:

$$\frac{31}{50}, \frac{32}{50}, \frac{33}{50}, \frac{34}{50}, \frac{35}{50}$$

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Q4. State whether the following statements are true or false. Justify your answers.

1. Every natural number is a whole number.
   ✅ True – Natural numbers are {1, 2, 3, 4, ...} and whole numbers include {0, 1, 2, 3, 4, ...}, so every natural number is a whole number.

2. Every integer is a whole number.
   ❌ False – Integers include negative numbers (-1, -2, -3, ...) which are not whole numbers.

3. Every rational number is a whole number.
   ❌ False – Rational numbers like $\frac{1}{2}$ and $-3.5$ are not whole numbers.

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