Rational Numbers

What is Rational Number

A rational numbers are numbers that can be expressed as a ratio of two integers.

All integers belong to the rational numbers. A rational number a/b is said to have numerator a and denominator b. Numbers that are not rational are called irrational numbers.

ab , b≠0

Where a and b are both integers.

Conditions for Rational Number

1. The limited number of digits after the decimal point.
For example, 5.4321.

2. The infinitely repeating number after the decimal point.
For example, 2.333333…

3. The infinitely repeating pattern of numbers after the decimal point.
For example, 3.151515…

Example:

• 3/7: Here 3 is an integer, 7 is an integer so yes it is a rational number.
• 0/0: Here there is 0 in the denominator. So it is not a rational number.
• -5: Here -9 can be written −5/1. So it is a rational number.
• 0: 0 is a rational number.
• 0.75 Here (3/4) can be written. So it is a rational number.
• 2.12 Here (212/100) can be written. So it is a rational number.

Positive Rational Numbers: If both the numerator and denominator have the same signs is called Positive Rational Numbers.
For example: + 2+ 5 , – 2– 5

Negative Rational Numbers: If both the numerator and denominator have different signs is called Negative Rational Numbers.
For example: + 2– 5 , – 2+ 5

Properties of Rational Number

1. A rational number remains unchanged when a non zero integer is multiplied to both numerator and denominator.

For example: 2 x 53 x 5 = 23

1. A rational number remains unchanged when a non zero integer is divided to both numerator and denominator.

For example: 2 ÷ 53 ÷ 5 = 23

If you have any doubts related to this topic, you can ask it into the comment section. If you have any problem in mathematics you can post your problem in the comment section. You will get a reply shortly.

I hope you have learned it properly.

Related Topic:

Irrational Number
Number System

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