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Is 4.55 a rational number?

  • Last Updated : 05 Aug, 2021

Numbers are frequently applied in our daily lives to conduct perfect calculations, count things, measurements, or recognizing time and for many other activities. They are also termed numerals.  The numerals help to conduct various arithmetic operations as addition, subtraction, multiplication, etc which are applicable in daily businesses and trading activities.

Numbers are generally expressed in terms of figures or words. For example, The numbers like 23, 50, and 100 represented in the form of figures can also be written as Twenty-three, Fifty, and One hundred respectively.  There are various types of numbers included in mathematics as prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc.

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Numbers are the mathematical values used for counting, measuring, and other arithmetic calculations. Some examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc.

The Number system or Numeral system is defined as a standardized system to express numbers. It is the unique way of representation in which numbers are represented in arithmetic and algebraic structure.

The value of a number is determined by:

  1. The digit
  2. Its place value in the number
  3. The base of the number system

Types Of Numbers

There are different types of numbers categorized into sets by the number system. The types are described below:

  • Natural numbers: Natural numbers are the positive integers that count from 1 to infinity. The set of natural numbers is denoted by ‘N’. It is the numbers we generally use for counting. The set of natural numbers can be represented as N={1,2,3,4,5,6,7,……………}
  • Whole numbers: Whole numbers are positive integers including zero, which counts from 0 to infinity. Whole numbers do not include fractions or decimals. The set of whole numbers is denoted by ‘W’. The set can be represented as W={0,1,2,3,4,5,………………}
  • Integers: Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals. The set of integers is denoted by ‘Z. The set of integers can be represented as Z={………..,-5.-4,-3,-2,-1,0,1,2,3,4,5,………….}
  • Decimal numbers: Any numeral value that consists of a decimal point is a decimal number. It can be expressed as 2.5,0.567, etc.
  • Real number: Real numbers are the set numbers that do not consist of any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R”.
  • Complex number: Complex numbers are numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
  • 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’.
  • 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’.

What are Rational Numbers?

The numbers which can be expressed as fractions or ratio of two integers and also can be written as a positive number, negative number, prime, and even zero is called rational numbers.

Rational numbers include all the positive integers (Non-negative integers), negative integers, and fractions or decimals with repeating digits after the decimal point such as 2/3,4/9,0.5,0.67…….etc.

A rational number can be expressed as p/q, where q ≠0.

Examples of Rational Numbers



Rational numbers include fractions or decimal expressions of the ratio of two integers. Some of the examples of rational numbers include

  • 5/3 is a rational number that can be expressed as 5 integers are divided by 3 integers.
  • 1/2 is a rational number that can be expressed as 1 integer is divided by 2 integers.

Is 4.55 a rational number?

Answer: 

Yes, the number 4.55 is a rational number. Since rational numbers can also be expressed as decimals with repeating digits after the decimal point. 

Take a look at the proof given below:

Proof:

The given number 4.55 can be expressed as

⇒450 =450/100

This can be further broken down as

⇒450/100 =9/2

The number 9/2 is the ratio of two integers that are 9 integers divided by 2 integers and expressed in fraction (as p/q where q is not equal to 0).

Similar Questions

Question 1: Is 0.5 a rational number?

Answer:

Yes, 0.5 is a rational number as its fractional expression will be 1/2 which is a ratio of two integers that is 1 and 2 respectively.

Question 2: Are all fraction values a rational number?

Answer:

Any fraction value which can be expressed as p/q where q is not equal to zero is a rational number. For example: 2/5, 1/2, etc.

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