- #1
jakey140
- 2
- 0
Is the number 1, or any other whole/negative number a rational number?
In summary: The definition of a rational number states that it can be expressed as a fraction of two integers, but sqrt(13) cannot be expressed in this form. Therefore, it is an irrational number. In summary, any integer is a rational number and the set of integers is a subset of the set of rational numbers. The square root of any number that is not a perfect square is irrational, including the square root of 13. Additionally, for a natural number n, the kth root of n is rational if and only if n can be expressed as m^k for some natural number m. The definition of a rational number is a number that can be expressed as a fraction of two integers, and this does not include sqrt(13).
- #2
radou
Homework Helper
- 3,149
- 8
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.
- #3
jakey140
- 2
- 0
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?
- #4
radou
Homework Helper
- 3,149
- 8
Find the definition of a rational number on the internet (or on this forum), it will clear some things up. 
- #5
fourier jr
- 765
- 13
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.
- #6
shmoe
Science Advisor
Homework Helper
- 1,994
- 1
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.
Similar statement for kth roots, n^(1/k) is rational if and only if n=m^k.
- #7
kar
- 1
- 0
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.
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.
FAQ: Rational Numbers: Is 1 a Rational Number?
What are rational numbers?
Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. This includes whole numbers, integers, and fractions.
Is 1 a rational number?
Yes, 1 can be expressed as the fraction 1/1, making it a rational number.
How are rational numbers different from irrational numbers?
Rational numbers can be written as a fraction, while irrational numbers cannot. Irrational numbers are non-repeating, non-terminating decimals, such as pi or the square root of 2.
Can rational numbers be negative?
Yes, rational numbers can be positive, negative, or zero. They simply need to be able to be expressed as a fraction.
What operations can be performed with rational numbers?
All basic arithmetic operations, including addition, subtraction, multiplication, and division, can be performed with rational numbers. They can also be expressed as decimals or percentages.
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