Question

Is 0.354355435554 rational or irrational or integer?

Answer 1

You have to look carefully at the decimal expression

Explanation:

Integer numbers do not have a decimal part, that is, they do not have decimals after the dot `'.'`. Examples are `-2, -53, 0, 4, 75` etc.

Rational numbers are the ones that can be written as a quotient of two integers `p/q`. Integers are in particular rational, because they can be written as `p/1`, as in `4/1, (-3)/1`, etc.

However, in terms of the decimal expression such as the one given in the problem, rational numbers can be expressed either with a finite number of decimals (such as `2.35, 79.5465989`), or periodic, such as `1/3=0.33333 ....`.

Irrational numbers cannot be written in the way above. Examples are `pi, sqrt(2), 1.12131415162728192021 ....`.

From all this you can say that the number given is not a integer and it is a rational number as it has a finite decimal expression

Answer 2

If `0.354355435554` ends after the last digit `4`, it is a rational number but if `0.354355435554....................` repeats the pattern endlessly, it is an irrational number.

Explanation:

If the number `0.354355435554` is limiting after `12` places of decimals, it is a rational number as

`0.354355435554=354355435554/1000000000000`.

However, apparently questioner is rather looking at

`0.354355435554....................`, which is clearly irrational as

grouping them as under reveals the pattern as follows:

`0.ul(354)color(red)(3554)ul(35554)....................`

Here we first have one `5` between `3` and `4`,

then we have two `5's` between `3` and `4`,

and then we have three `5's` between `3` and `4`.

Hence the number of `5's` between `3` and `4` is continuously increasing

and there is no group of numbers repeating endlessly

Hence `0.354355435554....................` is an irrational number.