What are Rational Numbers?

Different numbers are included in the number system, such as prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers are utilised in various arithmetic operations such as addition, subtraction, multiplication, division, percentage, etc. These numbers could be stated in multiple ways, including figures and words. Numbers are utilised in various arithmetic operations such as addition, subtraction, multiplication, and other functions used in everyday commerce and trading. The mathematical values used for counting, measuring, marking or recognising time and many other activities are numerals or numbers. Let’s discuss rational numbers in detail. 

What is a Rational Number? 

In mathematics, Any integer represented in the form p/q, where q!= 0 is zero, is a rational number. We can also classify any fraction as a rational number if the denominator and numerator are both integers and the denominator is not equal to zero. Whenever a rational number (i.e., a fraction) is divided, the output is in decimal form, which can be either ended or repeated.

How to Identify Rational Numbers?

To determine if a number is logical, examine the following criteria. The list is as follows:

• It should be written as p/q, where q is less than zero
• The p/q ratio could be simplified further and given as a decimal value
• Positive, negative, and zero are all included in the set of Rational Numerals. It’s easy to express it as a fraction

Positive and Negative Rational Numbers

Positive Rational Numbers

• If the denominator or numerator has the same sign
• All of them are greater than zero
• 12/7, 9/10, and 3/4, for example, are all positive rational numbers

Negative Rational Numbers

• If the numerator and denominator have the opposite sign
• All of them are smaller than zero
• Examples are negative rational numbers, such as -2/13, 7/-11, and -1/4

Properties of Rational Numbers

• You get the Rational Number Itself if you add a zero to a Rational Number
• A Rational Number can be added, subtracted, or multiplied to get another Rational Number
• When the numerator and denominator are multiplied or divided by the same factor, the rational values remain the same

Rational Numbers Vs Irrational Numbers

There is a distinction to be made between rational and irrational numbers. Rational Numbers are fractions with non-zero denominators. Irrational numbers refer to any numbers that are not rational. Positive, negative, or zero rational numbers exist. A negative Rational Number is specified by placing a negative sign in front of the numerator. Irrational numbers can’t be written as simple fractions, although they can be represented using a decimal. After the decimal point, there will be an infinite number of non-repeating digits.

Pi (π) = 3.142857…

√2 = 1.414213…

Standard Form of Rational Numbers

If there are no common factors between the dividend and divisor other than one, the standard form of a rational number could be determined, and the divisor is positive.

12/36, for instance, is a rational number. However, it can be simplified to 1/3 because there is only one common factor between the divisor and the dividend. As a result, the rational number 13 can be said to be in standard form.

How to Find the Rational Numbers between Two Rational Numbers?

Between two rational numbers, there exist “n” numbers of rational numbers. Two distinct strategies can find the rational numbers between two rational numbers. Let’s have a look at the two alternative approaches.

Method 1: 

Calculate the equivalent fractions of the given rational numbers and the rational numbers. Those figures should be the necessary rational figures.

Method 2: 

Calculate the mean of the two rational numbers supplied. The needed rational number should have been the mean value. Repeat the method with the old or newly obtained rational numbers to find more rational numbers.

Rational Numbers and Irrational Numbers

There are two types of numbers: rational and irrational. A rational number is a fraction having non-zero denominators. Because it is read as integer one divided by integer 2, the number 1/2 is rational. Irrational numbers are any numbers that are not rational.

Conclusion

The term “rational number” refers to a number that may be represented as a ratio of two integers. A number that cannot be stated in a ratio of two integers is called an irrational number. Both numerator and denominator of rational numbers are whole numbers, with the denominator not equal to zero. The rational numbers also include all integers, expressed as a quotient with the integer as the numerator and one as the denominator. I hope now you understand all about the rational number. You must go through the topic thoroughly; it will clear all your doubts.