The method to represent and work with numbers is understood as a numeration system or number system. A number system may be a system of writing to represent numbers. it’s the notation to represent numbers of a given set by using digits or other symbols. It allows us to work on arithmetic operations like division, multiplication, addition, subtraction. Some important number systems are as follows,
- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System
Let’s see about decimal number systems intimately.
Decimal Number System
The decimal numeration system consists of ten digits i.e. from 0 to 9. The bottom of the decimal numeration system is 10. These digits are often represented or expressed as any numeric value. For example, the decimal number 163 consists of the digit 3 in one place, the digit 5 in the tens place, and the digit 1 in hundreds place which can be represented as,
(1×102) + (6×101) + (3×100)
= (1×100) + (6×10) + (3) { where, 100 = 1}
= 100 + 60 + 3
= 163
The decimal number system is widely used in mathematics and there are different types of numbers based on the characteristics shown by them in the decimal system, for instance, there are real, complex, rational, irrational numbers, the following problems statement consist of knowledge related to irrational number, lets solve the problem,
Is 2 a Rational or Irrational number?
The above problem statement first requires to have the knowledge about what exactly rational and irrational numbers in the decimal number system are, therefore, lets first learn about rational and irrational numbers,
Rational Number
Rational numbers are numbers that may be represented as fractions and also as positive numbers, negative numbers, and 0. The real number is written within the p/q form, where q isn’t adequate to zero. For example, 3/2,5/3, and 1/7 are rational numbers.
Irrational Number
Irrational numbers are numbers that cannot be written in the form of fractions. They are represented in decimal form. For example, √19 = 4.35889, √2 = 1.424 are irrational numbers.
2 is a rational number because it satisfies the condition for rational number and can be written in p/q form which is mathematically represented as 2/1, where 1≠0.
Similar Problems
Question 1: Is 1/4 rational or an irrational number?
Answer:
1/4 is a rational number because it satisfies the condition for rational number and can be written in p/q form where, 4≠0.
Question 2: Is 1.5 a rational or an irrational number?
Answer:
1.5 is a rational number as it satisfies the condition for rational number and can be written as 3/2 which is in p/q form where, 2≠0.
Question 3: Is √2 a rational or irrational number?
Answer:
√2 is irrational number because it satisfies the condition for irrational number which is written in decimals i.e., the value of √2 = 1.4142135623730950…
Last Updated : 28 Feb, 2024
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...
FAQs
They are represented in decimal form. For example, √19 = 4.35889, √2 = 1.424 are irrational numbers. 2 is a rational number because it satisfies the condition for rational number and can be written in p/q form which is mathematically represented as 2/1, where 1≠0.
Is the number 2 a rational number? ›
A rational number is any number that can be expressed as a fraction or ratio of two integers. For example, 3/4, 8.75, 2, and -6 are all considered rational numbers. Note that integers, or "whole numbers", are rational numbers. This is because they can be expressed as fractions.
Is √ 2 is a rational number? ›
Sal proves that the square root of 2 is an irrational number, i.e. it cannot be given as the ratio of two integers.
Is 2 an irrational number? ›
X is an irrational number if it cannot be written as the ratio of two different integers. 2 can be written as 2/1, as there is a 1 under every integers. So 2 is not an irrational number.
Is 2 a real number? ›
The main difference between real numbers and the other given numbers is that real numbers include rational numbers, irrational numbers, and integers. For example, 2, -3/4, 0.5, √2 are real numbers. Integers include only positive numbers, negative numbers, and zero.
Is it must the difference between 2 rational numbers be a rational number? ›
The difference of two rational numbers is always a rational number as rational numbers are closed under subtraction.
Why is √ 2 an irrational number? ›
The square root of 2 is represented as √2. The actual value of √2 is undetermined. The decimal expansion of √2 is infinite because it is non-terminating and non-repeating. Any number that has a non-terminating and non-repeating decimal expansion is always an irrational number.
Is 3.14 a rational number? ›
Answer and Explanation:
The number 3.14 is a rational number. A rational number is a number that can be written as a fraction, a / b, where a and b are integers. The number pi is an irrational number.
Is 2 an integer number? ›
For example, 2,5,0,−12,244,−15 and 8 are all integers. The numbers such as 8.5,23 and 413 are not integers. (Note that a number can be an integer even if it is written as a decimal or a fraction: for example, −3.00 and 82 are both integers, because they are equal to −3 and 4 , respectively.)
Is √ 2 a real number? ›
Yes… The Real numbers range is Negative infinity to positive infinity including decimal numbers… i.e √2 is also real number..
Whether the circle is big or small, the value of pi remains the same. Pi can not be expressed as a simple fraction, this implies it is an irrational number. We know every irrational number is a real number. So Pi is a real number.
Is √ 2 a natural number? ›
Natural numbers are a subset of whole numbers, itself being a subset of integers, being a subset of rational numbers. I will prove, much more broadly, that the √2 is not rational, and is, in fact, irrational.
Is 2 a perfect square? ›
Theorem: Every positive integer is a perfect square! Proof: 1 is a perfect square. So, 2 is also a perfect square because 2=12+12 2 = 1 2 + 1 2 . Now, so is 3 , because 2 is a perfect square by our theorem and so is 1 .
Is 0 an integer? ›
That's right! All whole numbers are integers, so since 0 is a whole number, 0 is also an integer.
Is 11 2 a irrational number? ›
Examples of rational numbers are 1/2, 3/4, 11/2, 0.45, 10, etc. The examples of irrational numbers are Pi (π) = 3.14159…., Euler's Number (e) = (2.71828…), and √3, √2.
Is root 2 upon 3 a rational number True or false justify your answer? ›
False because √2 is an irrational number while 2 is a rational number so, any irrational number divided by rational number is irrational so √2/3 is an irrational number.
Is 2.5 a rational number justify your answer? ›
By definition, a rational number is one that can be written as a fraction or ratio between two integers (whole numbers). Since 2.5 can be written as the fraction 25/10, and both 25 and 10 are integers, 2.5 is a rational number.
Is 2 a rational number if 2 is an integer? ›
If 2 is an integer, then 2 is a rational number. This statement is true. 2 is indeed an integer, and all integers are rational numbers because they can be expressed as a fraction (in this case, 2/1).
What are rational numbers 2 examples? ›
Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on. The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational, since they give us infinite values.
