# Is 2.2360679774998... a rational, irrational, natural, whole, integer or real number?

##### 1 Answer

Jun 25, 2015

It's *real*.

It's NOT *integer* NOR *whole* (same as *integer*), NOR *natural* (*positive integer*).

#### Explanation:

It has decimal fractions, so it cannot be *integer* nor *whole*, nor *natural*.

Whether it is *rational* or *irrational* depends on what the ellipses at the end stand for.

*Rational* numbers in decimal notation are either *finite* or *infinite periodical*, while *irrational* numbers are *infinite non-periodical*.

It's not clear from the condition of this problem whether a fraction is periodical or not. My guess is that, since the period is not clearly marked (usually with parenthesis or a horizontal bar above it), it's more like non-periodical fraction, which makes an *irrational* number.

You can find it useful to study these issues at Unizor items "Algebra - Numbers".