Rational numbers

Rational number - is any number that can be written as a fraction: \[\frac{p}{q}\] where:

\(p \) - is any integer
\(q \) - integer different from \(0 \) (because we can't divide by zero).

Set of rational numbers is denoted \(\mathbb{Q}\) .

Formally set of rational numbers can be written in such a way: \[\mathbb{Q}=\left\lbrace\frac{p}{q}: p, q\in\mathbb{Z}\land q\ne 0\right\rbrace \]

Fact Every integer is a rational number.
Reason:

Every integer can be written as a fraction (and it's infinitely many ways!).

Przykład 1.

Number \(\frac{3}{4}\) is rational, because it is written in the form of a fraction.

Przykład 2.

Number \(1 \) is rational, because it can be written as a fraction: \[1 =\frac{1}{1}=\frac{4}{4}=\frac{17}{17}=\ ... \]

Przykład 3.

Number \(5 \) is rational, because it can be written as a fraction: \[5 =\frac{5}{1}=\frac{10}{2}=\frac{60}{12}=\ ... \]

Przykład 4.

Number \(- 3 \) is rational, because it can be written as a fraction: \[- 3 =\frac{-3}{1}=\frac{-6}{2 }=\frac{900}{- 300}=\ ... \]

Przykład 5.

Number \(0 \) is rational, because it can be written as a fraction: \[0 =\frac{0}{1}=\frac{0}{2}=\frac{0}{3}=\ ... \]

Przykład 6.

Number \(1\!\frac{7}{8}\) is rational, because it can be written as a fraction: \[1\!\frac{7}{8}=\frac{15}{8}\]

Przykład 7.

Number \(0{,}(3) \) is rational, because it can be written as a fraction: \[0{,}(3) =\frac{1}{3}\]

Przykład 8.

Number \(\sqrt{4}\) is rational, because it can be written as a fraction: \[\sqrt{4}= 2 =\frac{2}{1}\]

Przykład 9.

Number \(\sqrt [3]{125}\) is rational, because it can be written as a fraction: \[\sqrt [3]{125}= 5 =\frac{5 }{1}\]

Przykład 10.

Numbers: \(\sqrt{2},\ \sqrt{3},\ \pi \) are not rational.

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