Rational numbers

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Numbers

$a$

-5:

-5

-4:

-4

-3:

-3

-2:

-2

-1:

-1

equals: Zero

equals: One

-5/2:

-5/2

-3/2:

-3/2

-1/2:

-1/2

1/2:

1/2

3/2:

3/2

5/2:

5/2

-5/3:

-5/3

-4/3:

-4/3

-2/3:

-2/3

-1/3:

-1/3

1/3:

1/3

2/3:

2/3

4/3:

4/3

5/3:

5/3

-5/4:

-5/4

-3/4:

-3/4

-1/4:

-1/4

1/4:

1/4

3/4:

3/4

5/4:

5/4

-4/5:

-4/5

-3/5:

-3/5

-2/5:

-2/5

-1/5:

-1/5

1/5:

1/5

2/5:

2/5

3/5:

3/5

4/5:

4/5

Definition

The field of rational numbers $\mathbb{Q}$ is the field of fractions of the integers $\mathbb{Z}$.

Parameters

$a$

— rational number

Comments

(1)

The rational numbers form a field with respect to the usual addition and multiplication.

Programs

(P1)

Sage

numbers = [a/b for b in [1..5] for a in [-5..5] if gcd(a,b) == 1]

Links

[1]

Wikipedia: Rational number

Data properties

Entries are of type: rational number

Table is complete: no (it holds every $a/b$ in lowest terms with $|a| \leq 5$ and $1 \leq b \leq 5$, as examples of the field rather than as a reference list)

Repeats values from: Integers

How well the digits are known: exact

How they were obtained:

An exact value -- an integer, a rational or a polynomial -- so there is no precision to choose and nothing to be wrong about.