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# AP Board Class 9 Maths Chapter 1 Real Numbers

In chapter 1 of AP Board class 9 Maths textbook, students are basically introduced to the topic of real numbers. Usually, students learn about the definition of a real number and understand its different types like natural numbers, whole numbers, integers, fractions, rational numbers and irrational numbers. In addition to this, some of the other important topics discussed in chapter 1 include;

• Representing real numbers on a number line.
• Operations on real numbers.
• Properties of real numbers.
• Law of Exponents for real numbers.

## What is a Real Number?

A real number is a number which you can actually think of. Real numbers are also found on the number line and we normally use these numbers in real-world applications.

### Natural Numbers

Any counting number can be considered as natural numbers. These numbers lie on the right side of the number line after 0.

### Whole Numbers

Whole numbers are numbers without any decimal places or fractional parts. These number cannot be negative or have a negative value.

### Integers

An integer is basically a whole number and can be either positive, negative, or zero. Integers include natural or counting numbers.

### Fractions

A fraction is a part of a whole and generally represents an equal number of parts. They are located between integers in the number line.

### Rational Numbers

A rational number is a number that can be expressed as a ratio of two integers or in the form of a numerator upon a denominator. Rational numbers can be a whole number, a fraction, an integer and a natural number.

### Irrational Numbers

An irrational number is a number that is not rational. What it means is that it is a number that cannot be written in It is a non-terminating and non-repeating decimal.

Students can go through some of the chapter questions along with their solutions below to understand the topic more clearly;

Question 1: Are the following statements True? Give suitable reasons for your answers.

1. Are all rational numbers an integer.
2. All integers are rational numbers.
3. A rational number can be zero.

Solution:

1. False: For example, 6 and 9 are a rational number but not an integer.
2. True: Because any integer can be expressed in the form of
$$\begin{array}{l}\frac{p}{q}\left ( q\neq 0 \right )\end{array}$$
3. True: 0 can be expressed in a
$$\begin{array}{l}\frac{p}{q}\end{array}$$
form.

Question 2: Examine, whether the following numbers are rational or irrational

$$\begin{array}{l}(4+\sqrt{4})+(4-\sqrt{4})\end{array}$$

Solution:

$$\begin{array}{l}(4+\sqrt{4})+(4-\sqrt{4})\end{array}$$

=

$$\begin{array}{l}4+\sqrt{4}+4-\sqrt{4}\end{array}$$

= 8, which is a rational number

Question 3: Simplify

$$\begin{array}{l}\left ( 6\frac{1}{7} \right )^{^{4}}\end{array}$$

Solution:

$$\begin{array}{l}6\frac{4}{7}\end{array}$$

Question 4:  All real numbers are irrational. State whether the following statements are true or false. Justify your answers.

Answer:  The statement is false, since the real numbers are made up of rational and irrational members.

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