Question

Irrational numbers can never be precisely represented in a decimal form. Why is this?

Answer 1

Because irrational numbers are nonrepeating, otherwise they could be represented as a fraction. Although a potential counter-example to this claim is that some irrational numbers can only be represented in decimal form, for example, 0.1234567891011121314151617…, 0.24681012141618202224…, 0.101101110111101111101111110… are all irrational numbers.

Answer 2

A number is said to be irrational if decimal expansion of the number is non terminating non repeating.

Since decimal expansion is non terminating non repeating, so it can't be written precisely in decimal form.

For example

0.5674545678532........... or 0.101001000100001000001........

are Irrational number.So,it can't be expressed precisely in a decimal form.