# 1/3 - RATIONAL OR IRRATIONAL??

• Dec 19th 2008, 09:05 PM
1/3 - RATIONAL OR IRRATIONAL??
help i'm confused! 1/3 is a repeating decimal which i've been told is one of the ways to identify a number as irrational, but i know the definition of a rational number is a number that can be expressed as the ratio of two integers... well 1 and 3 are both integers.
i know there's other stipulations tho, like they cant both be divisible by the same prime, but that would be 1 and that would be true for any fraction of two decimals. so i'm a bit confused as to which 1/3 is. thanks for any help
• Dec 19th 2008, 09:16 PM
Chop Suey
Quote:

help i'm confused! 1/3 is a repeating decimal which i've been told is one of the ways to identify a number as irrational, but i know the definition of a rational number is a number that can be expressed as the ratio of two integers... well 1 and 3 are both integers.
i know there's other stipulations tho, like they cant both be divisible by the same prime, but that would be 1 and that would be true for any fraction of two decimals. so i'm a bit confused as to which 1/3 is. thanks for any help

A rational number is a number that can be expressed as a quotient of integers, or as a repeating or terminating decimal.

By repeating decimal, it is meant that there is a pattern for the decimals. For instance:
0.131313131313...
which is usually denoted (at least in my textbook) as $0.\overline{13}$

The "13" are repeating, and it can be shown (using infinite geometric series) that this infinite repetition of decimals can be expressed as:
$\frac{13}{99}$

1 is not a prime.
• Dec 19th 2008, 09:24 PM