Question

a real number is either a rational number or an irrational number. for example,
$\sqrt{2}$is a real number but it is not a rational number​

Answer 1

Step-by-step explanation:

Take a look at the definition of an irrational number. It is a real number thats value cannot be expressed by a ratio. This basically means any infinite decimal that isn’t a fraction.

Most common examples of irrational numbers are π, e, or √2. Their values, although can be determined precise enough for applied and practical real world uses, cannot be determined perfectly due to their infinite decimal points.

1/7 has a value of approximately 0.142857… which makes it appear irrational, but it is not irrational, since its exact value can be determined. A good trick to recognizing fractions between irrational numbers is that most fractions that create infinite decimals are actually just repeating decimals. 1/7 actually repeats the “142857”, the same way 1/3 repeats the number 3.

0.076923076923076923 may seem irrational, but its actually just 1/13. 3.141592653589793238 is irrational because the decimals never show any pattern.

πi is not irrational because it is imaginary. Simple as that.