Are repeating decimal irrational

Answer 1

No.

Repeating decimals are rational.

To convert a repeating decimal to a fraction, put the repeating digit(s) over the same number of 9s and simplify:

examples.

• 0.333...

It has one repeating digit (3) so put it over one 9 (9) to get 3/9 which can be simplified by dividing top and bottom by 3 (the hcf of 3 and 9) to get 1/3. Thus:

0.333... = 1/3

• 0.181818...

It has two repeating digits (18) so put them over two 9s (99) to get 18/99 which can be simplified by dividing top and bottom by 9 (the hcf of 18 and 99) to get 2/11. Thus:

0.181818.... = 2/11