Answer:
An irrational number may show terminating digits after the decimal
Step-by-step explanation:
Examples of Rational Numbers
Number 9 can be written as 9/1 where 9 and 1 both are integers. 0.5 can be written as ½, 5/10 or 10/20 and in the form of all termination decimals. √81 is a rational number, as it can be simplified to 9 and can be expressed as 9/1. 0.7777777 is recurring decimals and is a rational number
Examples of Irrational Numbers
Similarly, as we have already defined that irrational numbers cannot be expressed in fraction or ratio form, let us understand the concepts with few examples.
5/0 is an irrational number, with the denominator as zero.
π is an irrational number which has value 3.142…and is a never-ending and non-repeating number.
√2 is an irrational number, as it cannot be simplified.
0.212112111…is a rational number as it is non-recurring and non-terminating.
There are a lot more examples apart from above-given examples, which differentiate rational numbers and irrational numbers.
Properties of Rational and Irrational Numbers
Here are some rules based on arithmetic operations such as addition and multiplication performed on the rational number and irrational number.
#Rule 1: The sum of two rational numbers is also rational.
Example: 1/2 + 1/3 = (3+2)/6 = 5/6
#Rule 2: The product of two rational number is rational.
Example: 1/2 x 1/3 = 1/6
#Rule 3: The sum of two irrational numbers is not always irrational.
Example: √2+√2 = 2√2 is irrational
2+2√5+(-2√5) = 2 is rational
#Rule 4: The product of two irrational numbers is not always irrational.
Example: √2 x √3 = √6 (Irrational)
√2 x √2 = √4 = 2 (Rational)
(simplify:) 64