Question

Is 4.81 repeating an irrational number?

Answer 1

`4.818181818181.........` is not irrational.

Explanation:

A number in decimal fractions, whose a set of digits, after decimal point, repeat themselves endlessly, is always a rational number i.e. it is not irrational.

As in `4.818181818181.........` digits `81` after decimal point repeat endlessly, it is a rational number and hence not irrational.

A rational number number can always be represented as a ratio of two integers and so can `4.818181818181.........`

Let `x=4.818181818181.........` , then

`100x=481.818181818181.........`

Now subtracting former from latter, we get

`99x=481-4=477` and

`x=477/99`

Hence `4.818181818181.........` is not irrational.