Rational Numbers: Is 1 a Rational Number?

[jakey140]

Is the number 1, or any other whole/negative number a rational number?

 

[radou]

Every integer is a rational number, since for every integer a you can write a = a / 1. The set of integers is a subset of the set of rational numbers.

 

[jakey140]

Alright thanks a lot =).. so both negative and positive intgers are rational, also any fraction?... would the square root of 13 be classified as rational?

 

[radou]

Find the definition of a rational number on the internet (or on this forum), it will clear some things up.

 

[fourier jr]

i think the square root of any number that isn't a perfect square is irrational... maybe the square root of any power whose exponent is a power of 2 is rational. the square root of a prime is irrational for sure, & i think that can be proven the same way the square root of 2 is proven irrational.

 

[shmoe]

the square root of 13 is irrational. For a natural number n, sqrt(n) is rational if and only if n=m^2 for some natural number m.

Similar statement for kth roots, n^(1/k) is rational if and only if n=m^k.

 

[kar]

The definition of a rational number is: a number that can be expresed as a fraction p/q, where p and q are integers, q is not equal to 0.
Thus, any integer (positive and negative) is a rational number.
As for sqrt(13) - you can try and prove that it is not a rational number.