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Is 7.2 a rational number?

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Numeral System is a mathematical notation used for counting and calculating objects, and for executing arithmetic calculations. It is a writing system for representing numbers. It gives an exceptional depiction to every number and constitutes the arithmetic and algebraic form of the number. It allows us to operate arithmetic operations like addition, subtraction, multiplication, and division.

An equation is a declaration that joins two algebraic expressions of the same values with the ‘=’ sign. For example: In equation 8x + 4 = 7, 8x + 4 is the left-hand side expression and 7 is the right-hand side expression connected with the ‘=’ sign.

What is a Number?

A word or sign that designates an amount is known as a number. The numbers 4,6,8 etc. are even numbers and 3,5,7 etc. are odd numbers. A number is a value generated by a mixture of digits. These numbers are used to represent an algebraic number. A digit is an indication from a group of 10 numbers ranging from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Any combination of integers represents a number. The size of a Number depends on the count of digits that are used for its growth. For Example: 136, 198, 0.245, -16, 98, 96 etc.

Types of Numbers

Numbers are of various types depending upon the pattern of digits that are used for their development. Various characters and rules are also put in the Numbers which classify them into a diversity of different types,

Integers

Integers are a group of Whole Numbers plus the negative values of the Natural Numbers. Integers do not cover fraction numbers i.e. they can’t be written in a/b form. The scope of Integers is from the Infinity at the Negative end and Infinity at the Positive end, including zero. Integers are shown by the symbol Z. Integers are those digits whose fractional part is 0 like -5, -4, 1, 0, 20, 200.

Natural Numbers

Natural Numbers are numbers that scope from 1 to infinity. These numbers are also described as Positive Numbers or Counting Numbers. We can also show  Natural numbers by the symbol N. All the integers which are greater than 0 are natural numbers, Counting numbers like 5,6,7,8,9,10.

Whole Numbers

Whole Numbers are similar to Natural Numbers, but they also include ‘zero’.  Whole numbers can also be shown by the symbol W. Whole numbers include all natural numbers and 0 (zero).

Prime Numbers and Composite Numbers

All those numbers which are having only two definite components, the number itself and 1, are called prime numbers. All the numbers which are not Prime Numbers are known as Composite Numbers except 0. Zero is neither a prime nor a composite number. Some prime numbers are 3, 5, 7, 57, 51, 67, and 391. All numbers which are greater than 1 are composite numbers. Some composite numbers are 7, 5, 3, 17, 15, and 200.

Fractions

Fractions are the integers that correspond in the shape of a/b, where, a represent Whole numbers and b represent Natural Numbers, i.e., b can never be 0. The upper part of the fraction i.e. a is described as a Numerator whereas the lower part i.e. b is termed as Denominators. Example: -1/5, 0.25, 2/5, 18/4, …

Rational Numbers

Rational numbers are the numbers that can be shown in the fraction form i.e. a/b. Here, a and b both are numbers and b is not equal to 0. All the fractions are rational numbers but not all the rational numbers are fractions. Example: -2/5, 0.54, 1/5, 13/4, …

Irrational Numbers

Irrational numbers are the numbers that can not be shown in the form of fractions i.e. they can not be written as a/b. Example: √2, √3, √.434343, π…  

Real and Imaginary Numbers

Real numbers are numbers that can be shown in decimal form. These numbers involve whole numbers, integers, fractions, etc. All the numbers belong to Real numbers but all the real numbers do not belong to the integers. Imaginary Numbers are all those numbers that are not real numbers. These numbers when squared will show a negative number. The √-1 is represented as i. These numbers are also called complex numbers. Example: √-2, √-5,…

What are rational numbers?

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

It can be shown as p/q, where q ≠0

For example, 3/4 is a rational number that represents that 3 integers are divided by 4 integers.

Rational numbers can be represented as fractions, decimals, and even zero. All the numbers with a non-zero divisor which can be written in p/q form are rational numbers.

Let’s check out the different appearances of rational numbers

In fraction Form

A rational number is a ratio of two numbers that can be expressed in the form of p/q where q is not equal to zero. Hence, any fraction with a non-zero divisor is a rational number.

For an example:

4/5 is a rational number where 4 is a number being divided by a non-zero number that is 5.

In Decimal Form

A rational number can be also written in the decimal form if the decimal value is specific or has a repeating integer after the decimal point.

For example:

0.4 is a rational number. As the value 0.4 can be further written in the form of ratio or fraction as p/q

0.4 = 4/10

which is a ratio of two specific numbers.

Is 7.2 a rational number?

Solution:

Yes, 7.2 is a Rational Number. As rational numbers can be represented as decimals values as well as in the form of fractions.  The number can also be written as 72/10 which is the ratio of two numbers.

Take a look at the below solution.

The number 7.2 can be described as shown below:

=> 7.2 = 72/10

This can be additionally broken down as,

=> 720/100 = 36/5

The number 36/5 is the ratio of two number that are 36 digit divided by 5 digit and expressed in fraction form (as p/q where q is not equal to 0).

Similar Questions

Question 1: Is 4.5 a rational number?

Solution:

Yes, 4.5 is a Rational Number. As rational numbers can be represented as decimals values as well as in the form of fractions. The number can also be written as 45/10 which is the ratio of two numbers.

Take a look at the below solution.

The number 4.5 can be described as shown below:

=> 4.5 = 45/10

This can be additionally broken down as,

=> 450/100 = 9/2

The number 9/2 is the ratio of two number that are 4 digit divided by 5 digit and expressed in fraction form (as p/q where q is not equal to 0).

Question 2: Is 2.6 a rational number?

Yes, 2.6 is a Rational Number. As rational numbers can be represented as decimals values as well as in the form of fractions. The number can also be written as 26/10 which is the ratio of two numbers.

Take a look at the below solution:

The number 2.6 can be described as shown below:

=>2.6 = 26/10

This can be additionally broken down as,

=>260/100 = 13/5

The number 13/5 is the ratio of two number that are 4 digit divided by 5 digit and expressed in fraction form (as p/q where q is not equal to 0).

Question 3: Is 0 a rational number?

Answer:

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

Take a look at the below solution:

The digit 0 can be written as shown below:

=>0 = 0/1

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



Last Updated : 02 Jan, 2024
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