the product of two rational number is ‐ 15 by 56 if one of them is 5 by 8 find the other rational numberthe product of two rational number is minus 15 by 56 one of them is 5 by 5 by 8 find the other rational number
Answers
What is Rational number?
The rational numbers are numbers which can be expressed as a fraction and also as positive numbers, negative numbers and zero. It can be written as p/q, where q is not equal to zero.
Rational word is derived from the word ‘ratio’, which actually means a comparison of two or more values or integer numbers and is known as a fraction. In simple words, it is the ratio of two integers.
Example: 3/2 is a rational number. It means integer 3 is divided by another integer 2.
What is Irrational Number?
The numbers which are not a rational number are called irrational numbers. Now, let us elaborate, irrational numbers could be written in decimals but not in the form of fractions which means it cannot be written as the ratio of two integers.
Irrational numbers have endless non-repeating digits after the decimal point. Below is the example of the irrational number:
Example: √8=2.828…
How to Classify Rational and Irrational Numbers?
Let us see how to identify rational and irrational numbers based on below given set of examples.
As per the definition, the rational numbers include all integers, fractions and repeating decimals. For every rational number, we can write them in the form of p/q, where p and q are integers value.
Venn Diagram
Below image shows the Venn diagram of rational and irrational numbers which comes under real numbers.
Rational and Irrational Numbers
Difference Between Rational and Irrational Numbers
It is expressed in the ratio, where both numerator and denominator are the whole numbers
It is impossible to express irrational numbers as fractions or in a ratio of two integers
It includes perfect squares
It includes surds
The decimal expansion for rational number executes finite or recurring decimals
Here, non-terminating and non-recurring decimals are executed
Also, read: Difference Between Rational Numbers And Irrational Numbers
Examples
The list of examples of rational and irrational numbers are given here.
Examples of Rational Numbers
Number 9 can be written as 9/1 where 9 and 1 both are integers.
0.5 can be written as ½, 5/10 or 10/20 and in the form of all termination decimals.
√81 is a rational number, as it can be simplified to 9 and can be expressed as 9/1.
0.7777777 is recurring decimals and is a rational number
Examples of Irrational Numbers
Similarly, as we have already defined that irrational numbers cannot be expressed in fraction or ratio form, let us understand the concepts with few examples.
5/0 is an irrational number, with the denominator as zero.
π is an irrational number which has value 3.142…and is a never-ending and non-repeating number.
√2 is an irrational number, as it cannot be simplified.
0.212112111…is a rational number as it is non-recurring and non-terminating.
There are a lot more examples apart from above-given examples, which differentiate rational numbers and irrational numbers.