Is 1.3333 a rational number?

The method to represent and work with numbers is known as the number system. A number system is a system of writing to represent numbers. It is the mathematical notation used to represent numbers of a given set by using digits or other symbols. It has arithmetic operations to perform division, multiplication, addition, and subtraction between numbers. Some important number systems are as follows:

1. Decimal Number System
2. Binary Number System
3. Octal Number System
4. Hexadecimal Number System

Numbers and Digits  

Numbers are the counts or measurements used in mathematics, numerals are used to define numbers. A numeral can be defined as a symbol used for counting, for instance, there are 55 books in the library, where 56 is the numeral which is a combination of digits 5 and 6. A digit is a single numeral, the combination of digits form numerals. In the decimal number system, there are 10 digits, they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

What are Naturals Numbers?

In the Number system, Natural numbers are the numbers that start from 1 and count up to Infinity. For example – (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13, 14, 15, 16, 17, 18, 19, 20, 21..…….. ∞) are Natural Numbers.

Figure – 1

What are Rational Numbers?  

A rational number is a number that can be represented in a p/q form such that q is not equal to 0. The set of rational numbers Include positive, negative numbers, and zero and it is denoted by Q. Rational number can also be expressed as a fraction.

When a number is expressed in a p/q form or in fraction form where both the numerator and the denominator part are integers, then the number is known as a rational number.  

Some examples of rational numbers are: 1/2, -2/7, 7/10, -7/10, 14/99

The number “0” is also a rational number, as we can represent it in many forms such as 0/1, 0/2, 0/3, etc. But, 1/0, 2/0, 3/0, etc. are not rational numbers because they give us infinite values.

Note: Rational numbers can also be expressed in decimal form.  

Types of Rational Numbers

There are different types of rational numbers and they are:

Natural Numbers: All natural numbers are rational numbers because they can be written as in p/q form. Like 2 can be expressed in 2/1 (p/q) form.

Example – 1, 2, 3, 4, 5 …. etc.

Terminating Decimals: Rational numbers can also be expressed in decimal form because decimal numbers can be represented in p/q form. For example, 1.1 can be written as 1.1 = 11/10. Thus all terminating decimals are rational numbers.

Example – ( 0.45, 0.7120, 0.9778 etc. )

Non-Terminating Decimals: Non-Terminating decimals having repeated numbers after the decimal point such as 0.2222….., 0,12121212…. are also rational numbers. Since 0.222… can be written as 1/2, therefore it is a rational number.

Example – ( 0.22222….., 0.121212…..  etc. )

Fractions: When a number is expressed in a p/q form or in fraction form where both the numerator and the denominator part are integers, then it is a rational number.

Example – 3/4, 2/7, 7/10, -7/10, 14/99 (all of them are in p/q form)  

Whole Numbers: All whole numbers are rational numbers because the whole numbers can be expressed in p/q fraction form.

Example – 0 is a rational number because it can be written as a fin 0/1, 0/-2,… etc.

How to identify rational numbers?

There are some conditions to check whether a number is a rational number or not. They are:

1. Always it is represented in the p/q form, where q≠0. For example – 3/4 , 2/7,  7/10, -7/10, 0/1 etc.
2. A rational number can be further simplified and represented in decimal form. For example – 0.9, -0.875, 3.25, -2.0 etc.

Is 1.3333 a rational number?

Solution:

A rational number is a number that can be written in fraction form i.e. p/q form. Some of the fractions that have repeating decimals are considered rational numbers. Repeating decimals are considered rational numbers because they can be represented as the ratio form of two integers. Also, its decimal is terminating after some decimals.

Therefore 1.3333 is a rational number and can be written as p/q form that is 4/3.

Sample Questions

Question 1. Is 2.5 is a rational number?

Answer:

The decimal 2.5 is a rational number because it can be written as p /q form. All decimals can be converted to fractions. The decimal 2.5 is equal to the fraction 25/10.

Question 2. Identify whether Mixed Fraction 1 5/4 is a Rational Number or Not?

Answer:

The Simplest Form of Mixed fraction 1 5/4 is 9/4. It is in p/q form. Thus, 9/4 is a Rational Number.

Question 3. How to Identify a Rational Number?

Answer:

When a number is expressed in the p/q form where p, q are integers and q is non-zero then it is called a Rational Number.

Question 4. Is 20 a Rational Number?

Answer:

Yes 20 is a Rational Number because it can be expressed in 20/1 that is in p/q form.

Question 5. Is 0 a rational number?

Answer:

Yes, 0 is a rational number because it is an integer and It can be written in p/q form such as 0/1, 0/2, where b is a non-zero integer. Hence, 0 is a rational number.

Question 6. Is 1 a Rational Number?

Answer:

Yes, 1 is a Rational Number because it can be expressed in 1/1 that is p/q form.

Question 7. Is 5.3 a rational number?

Answer:

Yes 5.3 is a rational number.

Explanation: A rational number is any number that can be expressed as the quotient of two integers. In other words a rational can be expressed in p/q form. If a decimal representation terminates or recurs, then it is also expressible in the form  p/q for some integers p and q.

Question 8. What does it mean to be a terminating decimal?

Answer:

A decimal that can be expressed in a finite number of figures or those numbers which come to an end after a few repetitions after the decimal point are called terminating decimals.

Example: 0.1, 1.556, 123.456, etc.

Question 9. What do you mean by non – terminating decimal?

Answer:

Non-terminating decimals are those which keep on continuing after the decimal point or continue endlessly. They don’t come to end or if they do it is after a long interval. Then it is known as non – terminating decimals.

Example: 3.141592653589793238462643383279502884197169399375105820974….. ) is an example of a non-terminating decimal as it keeps on continuing after the decimal point.

Question 10. Is 9 an irrational number?

Answer: 

No, 9 is not an irrational number.

Explanation: An irrational number is a real number that cannot be expressed as a/b where a and b are integers. As 9/1 = 9 and 9 and 1 are integers, this means 9 is not an irrational number.