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Is 3.27 a Rational or Irrational number?

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  • Last Updated : 09 Mar, 2022

The number system includes different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures as well as words accordingly. For example, the numbers like 40 and 65 expressed in the form of figures can also be written as forty and sixty-five.

Number system

A Number system or numeral system is defined as elementary system to express numbers and figures. It is the unique way of representation of numbers in arithmetic and algebraic structure. Numbers are used in various arithmetic values applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc which are applicable in daily lives for the purpose of calculation. The value of a number is determined by the digit, its place value in the number, and the base of the number system.

Numbers generally are also known as numerals are the mathematical values used for counting, measurements, labeling, and measuring fundamental quantities.

Rational numbers

Rational numbers are the numbers that can be expressed as the ratio of two integers. It includes all the integers and can be expressed in terms of fractions or decimals. It is denoted by ‘Q’. Examples of Rational Numbers,

  1. Number 5 can be written as 5/1 where 5 and 1 both are integers.
  2. 0.6 can be written as 3/5, 6/10 or 60/100 and in the form of all termination decimals.
  3. √49 is a rational number, as it can be simplified to 7 and can be expressed as 7/1.
  4. 0.66666 is recurring decimals and is a rational number

Irrational numbers

Irrational numbers are numbers that cannot be expressed in fractions or ratios of integers. It can be written in decimals and have endless non-repeating digits after the decimal point. It is denoted by ‘P’. Examples of Irrational Numbers,

  1. 4/0 is an irrational number, with the denominator as zero.
  2. π is an irrational number which has value 3.142…and It shows a result that is a never-ending and non-repeating number.
  3. √3 is an irrational number, as it cannot be simplified.
  4. 0.3131548525 …is a rational number as it is non-recurring and non-terminating. 

Is 3.27 a rational or irrational number?

Answer:

Rational numbers are of the form p/q, where p and q are integers and q ≠ 0. Because of the underlying structure of numbers, p/q form, most individuals find it difficult to distinguish between fractions and rational numbers. When a rational number is divided, the output is in decimal form, which can be either ending or repeating. 3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1.

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

Here, the given number, 3.27 can be expressed  in the form of p/q, and we can write 3.27 as 327/100.

Hence, 3.27 is a rational number.

Similar Questions 

Question 1: How is 1.57 a rational number?

Answer:

Here, the given number, 0.57 can be expressed  in the form of p/q, and we can write 1.57 as 157/100.

Hence, 1.57 is a rational number.

Question 2: Determine whether 6.1616…. is a rational number.

Answer:

Here, the given number, 6.1616…. has recurring digits. Hence, 6.1616… is a rational number.

Question 3: Is 4.82 a rational number or an irrational number?

Answer:

Here, the given number, 4.82 can be expressed in the form of p/q as 4.82 = 482/100 = 241/50 and has terminating digits. Hence, 4.82 is a irrational number.

Question 4: Determine whether 5.2544848 is a rational number or an irrational number.

Answer:

Here, the given number 5.2544848 is an irrational number as it has non terminating and non recurring digits.

Question 5: Determine whether the product of √3 × √4 is rational or irrational?

Answer: 

Given: √3 × √4 both are irrational numbers but it is not necessary that the product of two irrational number will be irrational.

Therefore √3 × √4

= √12

But here square root of 12 is 3.464101… which is non terminating and non recurring after decimal.

Hence the product of √3 × √4 is irrational.

Question 6: Determine whether the product of √3 x √3 is rational or irrational?

Answer: 

Given: √3 × √3 both are irrational numbers but it is not necessary that the product of two irrational number will be irrational

Therefore √3 × √3

= 9 as it is a perfect square of 3.

But here square root of 9 is 3 which is a whole number and terminated.

Hence the product of √3 × √3 is rational.

Question 7: Determine whether 2.183183… is a rational number.

Answer:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, 2.183183… has recurring digits.

Hence, 2.183183… is a rational number.

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