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Is the real number 1.21 rational or irrational?

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  • Last Updated : 27 May, 2022

The set of rational and irrational numbers is termed Real numbers. They can be both positive or negative and are represented by the sign “R.” This set includes all natural numbers, decimals, and fractions. This module includes all natural numbers, decimals, and fractions. In the number system, real numbers are essentially the combination of rational and irrational numbers. In general, all arithmetic operations may be performed on these numbers, and they can also be represented on a number line. Any number that can be represented as a fraction p/q is termed as a rational number. In this fraction the numerator value is written as ‘p,’ while the denominator value is represented as ‘q,’ where ‘q’ is not equal to zero.  Natural numbers, whole numbers, a decimal, or an integer all are part of rational numbers.

Examples: 1/2, -2/3, 0.5, and 0.333 are all rational numbers.

Irrational numbers are real numbers that cannot be represented as a fraction p/q, where ‘p’ and ‘q’ are integers, and the denominator ‘q’ is greater than zero (q≠0). 

Examples: (pi) is an irrational number π = 3.14159265… The decimal number, in this case, never ends at any point. Therefore numbers like √2, √-7, and so on are irrational numbers.

Is the real number 1.21 rational or irrational? 

Solution: 

Any number that can be represented as a fraction p/q is termed as a rational number. when the number is simplified it gives the result in decimals which is either terminating or recurring after decimal.

So, here given number real number 1.21 is rational number as it is terminating after decimal.

Sample Questions

Question 1: Determine whether -55 is a rational number.

Solution:

Any number that can be represented as a fraction p/q is termed as a rational number. when the number is simplified it gives the result in decimals which is either terminating or recurring after decimal.

So, here given number -55 is rational number as it is terminating after decimal.

Question 2: Is 23.25 a rational number or an irrational number?

Solution:

Any number that can be represented as a fraction p/q is termed as a rational number. when the number is simplified it gives the result in decimals which is either terminating or recurring after decimal.

So, here given number 23.25 is rational number as it is terminating after decimal.

Question 3: Determine whether 2/51 is a rational number or an irrational number.

Solution: 

Any number that can be represented as a fraction p/q is termed as a rational number. when the number is simplified it gives the result in decimals which is either terminating or recurring after decimal.

So, here given number 2/51 is in fraction form and rational number can be expressed as a fraction, Therefore,

2/51 is a rational number.

Question 4: Is 7.656545 is a rational number?

Solution:

Any number that can be represented as a fraction p/q is termed as a rational number. when the number is simplified it gives the result in decimals which is either terminating or recurring after decimal.

Irrational numbers are real numbers that cannot be represented as a fraction p/q, where ‘p’ and ‘q’ are integers and the denominator ‘q’ is greater than zero (q≠0). So, here given number 7.656545 is a rational number, as it is terminating after decimal at ending point.

Question 5: Is 0.23224554… a rational number?

Solution:

Any number that can be represented as a fraction p/q is termed as a rational number. when the number is simplified it gives the result in decimals which is either terminating or recurring after decimal.

Irrational numbers are real numbers that cannot be represented as a fraction p/q, where ‘p’ and ‘q’ are integers and the denominator ‘q’ is greater than zero (q≠0). So, here given number 0.23224554…. is not a rational number, its a irrational number as it is non terminating or non recurring after decimal.

Question 6: Is Real number 2.8899898 a rational number?

Solution:

Any number that can be represented as a fraction p/q is termed as a rational number. when the number is simplified it gives the result in decimals which is either terminating or recurring after decimal. Irrational numbers are real numbers that cannot be represented as a fraction p/q, where ‘p’ and ‘q’ are integers and the denominator ‘q’ is greater than zero (q≠0).

So, here given number 2.8899898 is a rational number as it is terminating after decimal at ending point.

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