All real numbers are rational numbers.
A) True
B) False
Answer
638.4k+ views
Hint:
We will first define the real number and rational number. Real numbers are numbers which are formed from the combination of both rational numbers and irrational numbers and rational number is defined as a number which can be expressed in the form of $\dfrac{p}{q}$, where $p$ and $q$ are integers and $q$ cannot be zero. We will use these definitions to check the given statement.
Complete step by step solution:
Here we need to check whether all real numbers are rational numbers or not.
We know that the real numbers are numbers which are formed from the combination of both rational numbers and irrational numbers and rational number is defined as a number which can be expressed in the form of $\dfrac{p}{q}$ , where $p$ and $q$ are integers and $q$ cannot be zero
Thus, we can say that numbers which are not rational numbers are called irrational numbers.
If we combine the rational numbers and the irrational numbers, we get real numbers.
Hence, all real numbers are not rational numbers because real numbers also contain irrational numbers.
Hence, the given statement is false.
Therefore, the correct option is option B.
Note:
Rational and irrational are opposite to each other. Rational numbers can be expressed as the ratio of two integers - hence the name rational. An Irrational is any number which is not rational. So every rational number is certainly not irrational. Rational numbers and irrational numbers are mutually exclusive. Therefore, every rational number is sure not to be a irrational number and every irrational number is sure not to be a rational number.
We will first define the real number and rational number. Real numbers are numbers which are formed from the combination of both rational numbers and irrational numbers and rational number is defined as a number which can be expressed in the form of $\dfrac{p}{q}$, where $p$ and $q$ are integers and $q$ cannot be zero. We will use these definitions to check the given statement.
Complete step by step solution:
Here we need to check whether all real numbers are rational numbers or not.
We know that the real numbers are numbers which are formed from the combination of both rational numbers and irrational numbers and rational number is defined as a number which can be expressed in the form of $\dfrac{p}{q}$ , where $p$ and $q$ are integers and $q$ cannot be zero
Thus, we can say that numbers which are not rational numbers are called irrational numbers.
If we combine the rational numbers and the irrational numbers, we get real numbers.
Hence, all real numbers are not rational numbers because real numbers also contain irrational numbers.
Hence, the given statement is false.
Therefore, the correct option is option B.
Note:
Rational and irrational are opposite to each other. Rational numbers can be expressed as the ratio of two integers - hence the name rational. An Irrational is any number which is not rational. So every rational number is certainly not irrational. Rational numbers and irrational numbers are mutually exclusive. Therefore, every rational number is sure not to be a irrational number and every irrational number is sure not to be a rational number.
Recently Updated Pages
What is BLO What is the full form of BLO class 8 social science CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

10 examples of friction in our daily life

Draw a diagram of nephron and explain its structur class 11 biology CBSE

Write structures of the following compounds i 2 Chloro3methylpentane class 11 chemistry CBSE

A Paragraph on Pollution in about 100-150 Words

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Name 10 Living and Non living things class 9 biology CBSE

What is the full form of pH?

What is pollution? How many types of pollution? Define it

What is momentum with examples class 9 physics CBSE

