The real number system is an important topic in Class 10 Maths. It helps us understand different kinds of numbers. In simple words, real numbers are all the numbers that can be shown on a number line.
For example, -3, 0, 2, 1/2, 4.5, √2, and π are real numbers.
What Are Real Numbers?
First, let us understand the main idea. Real numbers are divided into two main groups:
- Rational Numbers
- Irrational Numbers
Together, these two groups make the real number system.
Rational Numbers
A rational number is a number that can be written in the form p/q, where q is not zero.
For example:
- 2 = 2/1
- 5 = 5/1
- 1/2
- 3/4
- -7/2
Therefore, these are all rational numbers.
Some decimal numbers can also be rational numbers. For example, 0.5 = 1/2. Similarly, 0.75 = 3/4.
Irrational Numbers
Next, we have irrational numbers. These numbers cannot be written in the form p/q.
For example:
√2 = 1.414213…
The decimal numbers continue without ending and do not repeat in a fixed pattern. Therefore, √2 is an irrational number.
Other examples are √3, √5, and π.
Example of the Real Number System
Let us take four numbers:
3, -4, 1/2, and √2
First, 3 is a rational number because it can be written as 3/1.
Next, -4 is also rational because it can be written as -4/1.
Similarly, 1/2 is a rational number.
However, √2 is an irrational number.
Even though they are different types of numbers, all four are real numbers.
Real Numbers on a Number Line
A number line helps us see real numbers clearly.
For example:
-3 — -2 — -1 — 0 — 1 — 2 — 3
Negative numbers are placed on the left of zero. On the other hand, positive numbers are placed on the right of zero. Fractions and irrational numbers can also be shown on a number line.
Why Is the Real Number System Important?
The real number system is useful in many parts of Class 10 Mathematics. It helps us understand numbers, solve equations, and work with different Maths problems.
Finally, remember this simple rule:
Real Numbers = Rational Numbers + Irrational Numbers
In short, if a number can be represented on a number line, it is a real number.