The rational numbers are the numbers that are mainly written as ratio and can be identified as ration numbers. The numbers can be identified as rational which can be written as fraction where there is numerator as well as there is denominator and both the numbers are whole numbers.
All the whole numbers in the number systems can be identified as the rational numbers as because all the whole numbers can be written as fractions.
A rational number is considered as part that is expressed as a fraction, decimal as well as percentage. A number is considered to be rational where the number is written as fraction where both the numerators and the denominators of the rational numbers are whole numbers. The rational number is mainly derived from a word ratio. This is because the rational numbers are mainly written in the form of a ratio. All the whole numbers in the number system that includes negative numbers, positive numbers as well as zero are considered as rational number. Any whole number is considered as rational number as because all whole numbers can be written in n/1 form.
Examples of rational numbers are:
3 = 3/1, where 3 is considered as rational numbers.
There are many such rational numbers such as 3/8, -5/4 as because the numerators as well as denominators in the fractions are whole numbers.
There are recurring decimals also in rational numbers. Example- 0.454545454.
It can be summarized that rational numbers are generally derived is ratio that mainly compares two main quantities and is considered or is expressed in the simple fraction form. The integers and the denominators in the rational number is natural number that includes mixed fraction, recurring fraction, as well as finite fractions in the system.
The numbers that cannot be identified as rational numbers can be considered as irrational numbers. Irrational numbers are mainly written as the decimal numbers and are not written as a fraction. The irrational numbers can be identified as decimal numbers that has endless no-repeating numbers written on the right of decimal point. The irrational numbers are not actually used in the daily number systems but the numbers do exists on number line. There are many irrational numbers in between 0 and 1.
The irrational numbers is considered as a number that does not satisfy the constraints of rational number. The irrational numbers cannot be written as in the form of ratio between two different numbers.
Square root of 2 is an example of irrational number as because the number of root 2 cannot be defined or written in the ratio form between the two integers. The square root of number 2 is not considered as a whole number, or neither as fraction or decimal. The irrational numbers are generally square roots of all the non-perfect squares. Pi is also considered as an example of irrational numbers. Pi has repeating decimal number which is known as irrational number. Surds are basically known as irrational numbers.
It can be summarized that if a number cannot be defined in the form of fraction, those numbers are known as irrational numbers. These numbers cannot be written in the form of integer or a natural number. The decimal part of the number is generally recurring or is non-finite in the irrational number.
|Rational Numbers||Irrational Numbers|
|The meaning of rational numbers can be defined as a number that are generally expressed as a ratio of two particular numbers.||The definition of irrational numbers consists of one that cannot be written as the ratio of the two numbers.|
|The fraction that is included in rational numbers is mainly expressed as fraction where the denominator cannot be defined as 0.||The irrational numbers cannot be defined as fraction.|
|The rational numbers are not perfect squares.||The irrational numbers are mainly considered as surds.|
|The decimal expansion included in rational numbers are finite and includes recurring decimals.||The decimal expansions in the irrational numbers mainly includes non-finite as well as non-recurring decimals.|
|Example of rational number:||Example of irrational number:|
|1. The number 8 is considered as rational number because the number can be written as 8/1.||1. π = 3.141592|
|2. ¾ can also be considered as rational number as it can be written as a fraction.||2|
The rational number mainly includes those decimals that are finite as well as repeating. The irrational numbers mainly includes all those numbers that states decimal expansion that is infinite as well as non-repetitive as well as does not have y pattern in the number.
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