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Is zero a rational number?

  • Last Updated : 05 Aug, 2021

Numerals or numbers are the arithmetical values used for counting, measurements, or recognizing time and for many other activities. Numerals are generally called numbers. The numerals are used in various arithmetic operations as addition, subtraction, multiplication, etc which are applicable in daily businesses and trading activities.

Numbers can be expressed in the form of figures as well as words respectively as required. The number system involves various types of numbers for example real numbers, complex numbers, even numbers, rational numbers, whole numbers, etc.

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

The Number system is a system for the representation of numbers, which includes categories like, zero, negative numbers, rational numbers, irrational numbers, and complex numbers.

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:

  1. Natural numbers: Natural numbers are the positive counting numbers 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,……………
  2. Whole numbers: Whole numbers are positive counting numbers 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,………………
  3. 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,………….
  4. 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.
  5. The real number: Real numbers are the set numbers that do not include any imaginary value. It includes all the positive integers, negative integers, fractions, and decimal values. It is generally denoted by ‘R”.
  6. Complex number: Complex numbers are sets of numbers that include imaginary numbers. It can be expressed as a+bi where “a” and “b” are real numbers. It is denoted by ‘C’.
  7. 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’.
  8. 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’.

Rational Numbers

A Rational number is defined as a real number in the form of A/B where B is not equal to zero. In simple words, we can state that any fraction with a non-zero denominator is a rational number.

Rational numbers involve all positive integers, negative integers. Even 0 is rational as it has a non-zero denominator.

The mathematical representation of the rational numbers is as A/B

Where,



B is not equal to Zero(0)

Some Examples of Rational Numbers

Rational numbers are fractional or decimal values. Some of the examples of rational numbers are

  • 2/5 is a rational number that is a ratio of two integers 2 and 5.
  • 0.5 is a rational number that can also be written as 1/2 which is the ratio of two integers 1 and 2.

Now let’s jump into the question.

What are rational numbers?

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

It can be expressed by p/q, where q ≠0

For example, 5/3 is a rational number that expresses that 5 integers are divided by 3 integers.

What are 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.

For example: √15 =3.8729…….. 

Is 0 a rational number?

Answer: Yes, 0 is a rational number because it has a non-zero denominator. Since the number 0 can also be written as 0/1.

Take a look at the below proof.



Proof:

The number 0 can be represented as shown below:

⇒ 0 = 0/1

From the above expression, we can conclude that the number 0 can be expressed in the form of p/q where q is not equal to zero.

Similar Questions

Question 1: Does the ratio of any two integers makes a rational number?

Answer:

No, a number is said to be rational only if it has a non-zero denominator. 

Question 2: Is 2.5 a rational number?

Answer:

Yes, 2.5 is a rational number because the number can also be expressed 25/10 which a ratio of integers.

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