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Why every rational number is not a whole number?

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  • Last Updated : 05 Apr, 2022

Numbers are mathematical values or numbers that are used to measure or calculate quantities. It is represented by numerals such as 2, 4, 7, and so on. Integers, whole numbers, natural numbers, rational and irrational numbers, and so on are instances of numbers. There are several sorts of numbers in the number system, such as prime numbers, odd numbers, even numbers, rational numbers, whole numbers, and so on. These figures and words can be used to convey these figures and words. For example, integers such as 40 and 65 stated as figures can alternatively be written as forty and sixty-five. 

A number system, often known as a numeral system, is a basic framework for expressing numbers and figures. It is a distinct method of expressing numbers in arithmetic and algebraic structures.

Why every rational number is not a whole number? 

Answer: 

To answer this we have to understand the concept of Whole number and Rational number.

Whole Numbers 

Whole numbers are the subset of numbers comprising zero and all positive integers. The entire number ranges from 0 to infinity. These numbers are required in day-to-day calculations, mostly for measuring fundamental quantities. Whole numbers, including zero, are the only constituents of natural numbers. The subset is represented by the numbers 0, 1, 2, 3, 4, 5, … Fractions, decimals, and negative integers are not included in the subset.

Examples of whole number: Positive integers, often known as counting numbers, are portions of whole numbers that include zero, such as 0,1, 2, 3, 4, 5, and so on, omitting negative integers, fractions, and decimals. Whole numbers include 10, 11, 22, 100, 1000, and so on.

Rational Number 

Rational numbers have the form p/q, where p and q are integers and q ≠ 0. Most people find it difficult to discern between fractions and rational numbers because of the underlying structure of numbers, p/q form. When a rational number is split, the result is a decimal number that might be ending or recurring. 

Examples of rational numbers are 9, 8, 7, and so on, which may be written in fraction form as 9/1, 8/1, and 7/1, respectively.

Every Rational number is not a whole number because A whole number is a component set of zero and all positive numbers such as 0, 1, 2, 3, 10, 15,… include only positive integers. It excludes negative integer, decimal, and fractional values . 

Rational Number includes all the fractions, integers as well as decimal numbers.

Here set of whole number like 3, 4, 5 we can write this number as a fraction of 1 like 3/1, 4/1, 5/1… in ratio of two integers. Therefore every whole number is a rational number but every rational number is not a whole number.

Similar Questions

Question 1: Identify whole numbers and Rational numbers?

35, 48.09, 2/9, 16898

Answer:

A whole number is a component set of zero and all positive numbers such as 0, 1, 2, 3, 10, 15,… include only positive integers. It excludes negative integer, decimal, and fractional values. 

Rational Number includes all the fractions, integers as well as decimal numbers. Here 35 and 16898 are the two whole numbers and 48.09, 2/9 are rational numbers.

Question 2: How is 2.57 a rational number?

Answer:

Here, the given number, 2.57 can be expressed in the form of p/q, and we can write 2.57 as 257/100.

Hence, 2.57 is a rational number.

Question 3: Is -6.82 a rational number or an irrational number?

Answer:

Here, the given number, 6.82 can be expressed in the form of p/q as,

6.82 = 682/100 

= 341/50 and has terminating digits. 

Hence, 6.82 is a rational number.

Question 4: Is 8/4 a rational number or a whole number?

Answer:

Here, the given number, 8/4 is in the form of p/q.

Therefore 8/4 = 2 

Which is a whole number and has terminating digits. 

Hence, 8/4 is a rational number.

Question 5:  Determine whether 9.5682949 is a rational number or an irrational number.

Answer:

Here, the given number 9.5682949 is an irrational number as it has non terminating and non recurring digits. Here, after the decimal points, the numbers present are terminating and are also not repeating in nature.

Question 6:  Determine whether -7 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.

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’.

Hence, -7 is an integer and it is a rational number.

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