# Thread: 1/3 - RATIONAL OR IRRATIONAL??

1. ## 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

2. Originally Posted by potato salad123
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 $\displaystyle 0.\overline{13}$

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

1 is not a prime.

3. cool, so basically both rational and irrational numbers can have infinite decimal places but the irrationals MUST have infinite decimal places? that mighta been where i got confused.

4. Originally Posted by potato salad123
cool, so basically both rational and irrational numbers can have infinite decimal places but the irrationals MUST have infinite decimal places? that mighta been where i got confused.
Read this: Decimal - Wikipedia, the free encyclopedia

A rational number has a recurring decimal representation, an irrational number does not.