Relacionando fracciones y decimales

1. Expresando fracciones como decimales

En la sección anterior hemos visto que una fracción se puede interpretar como una división. Recordemos el ejemplo:

Una botella de tres cuartos de litro se puede decir que es una botella de 0,75 litros.

\( \Large \displaystyle \frac {3} {4} = 0,75\hspace{1mm} \text{L}\hspace{1mm}= 75\hspace{1mm} \text{cl}\)

(si realizamos la división \(3:4 = 0,75 \) )

Es decir, el valor de una fracción se puede expresar como un número decimal. Bastaría con realizar la división del numerador entre el denominador, ¡y la división ya la tenemos controlada! ¿Cómo pueden ser eses decimales resultantes? ¡Veámoslos!

Lectura facilitada

El valor de una fracción se puede expresar como un número decimal,

bastaría con realizar la división del numerador entre el denominador.

Una botella de tres cuartos de litro se puede decir que es una botella de 0,75 litros.

\( \Large \displaystyle \frac {3} {4} = 0,75\hspace{1mm} \text{L}\hspace{1mm}= 75\hspace{1mm} \text{cl}\)

(si realizamos la división \(3:4 = 0,75 \) )

2. Tipos de números decimales

Para ver cómo expresar una fracción como un decimal, y viceversa, necesitamos saber qué tipos de números decimales existen:

Lectura facilitada

3. ¿De qué tipo de decimal se trata?

¡La inspectora Cruxeiras nos reta para ver si somos expertos en la clasificación de decimales!

Seleccionad la respuesta correcta

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1 2 3 4 5 6 7 8 9

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4. Expresando decimales como fracciones: Decimal exacto a fracción

Del mismo modo, podremos expresar un decimal racional (exacto o periódico) como una fracción, que llamaremos fracción generatriz.

En este REA nos centraremos en ver cómo transformar un número decimal exacto en una fracción:

El proceso es muy sencillo, puesto que podemos transformarlo como una división entre 10, 100, 1000..., siempre fijándonos en la cantidad de cifras decimales que contiene el número. Veámoslo con tres sencillos ejemplos:

\( \Large 0,9 = \frac{9}{10} \) (Una sola cifra decimal -> transformamos en una división entre 10)

\( \Large 0,37 = \frac{37}{100} \) (Dos cifras decimales -> transformamos en una división entre 100)

\( \Large 1,369 = \frac{1369}{1000} \) (Tres cifras decimales -> transformamos en una división entre 1000)

Lectura facilitada

Podemos expresar un decimal racional (exacto o periódico) como una fracción,

que llamaremos fracción generatriz.

Nos centraremos en ver cómo transformar un número decimal exacto en una fracción:

Podemos transformarlo como una división entre 10, 100, 1000...,

siempre fijándonos en el número de cifras decimales que contiene el número.

Ejemplos:

\( \LARGE 0,9 = \frac{9}{10} \) (Una sola cifra decimal -> transformamos en una división entre 10)

\( \LARGE 0,37 = \frac{37}{100} \) (Dos cifras decimales -> transformamos en una división entre 100)

\( \LARGE 1,369 = \frac{1369}{1000} \) (Tres cifras decimales -> transformamos en una división entre 1000)

La inspectora Cruxeiras reflexiona en alto

Un decimal se puede expresar con distintas fracciones, siempre que estas sean equivalentes. Ejemplo:

\( \Large 1,25 = \frac{125}{100} = \frac{25}{20} = \frac{5}{4} \) -> Fracción irreducible

En este caso lo que hemos hecho es simplificar la fracción de partida. Para simplificar fracciones recuerda que debemos dividir numerador y denominador por el mismo número. En este caso dividimos primero por 5 y luego, de nuevo, por 5, hasta llegar a una fracción que no podemos simplificar, es decir, llegamos a una fracción irreducible.

Por esta razón, siempre que nos pidan calcular la fracción generatriz de un número decimal, debemos expresarla a través de su fracción irreducible, ¡así que no te olvides de simplificar!

Lectura facilitada

Un decimal se puede expresar con distintas fracciones,

siempre que estas sean equivalentes.

\( \LARGE 1,25 = \frac{125}{100} = \frac{25}{20} = \frac{5}{4} \) -> Fracción irreducible

Para simplificar fracciones recuerda que debemos

dividir numerador y denominador por el mismo número.

Siempre que nos pidan calcular la fracción generatriz

de un número decimal debemos expresarla a través

de su fracción irreducible, ¡así que no te olvides de simplificar!

5. Transforma los siguientes decimales

Calcula la fracción generatriz :

\(\large{a)\hspace{1 mm} 0,3}\)

\(\large{b)\hspace{1 mm} 1,7}\)

\(\large{c)\hspace{1 mm} 0,197}\)

\(\large{d)\hspace{1 mm} 0,4}\)

\(\large{e)\hspace{1 mm} 0,25}\)

\(\large{f)\hspace{1 mm} 1,2}\)

\(\large{g)\hspace{1 mm} 25,55}\)

\(\large{h)\hspace{1 mm} 0,74}\)

\(\large{i)\hspace{1 mm} 9,68}\)

Mostrar respuestas

\(\large{a)\hspace{1 mm} \frac{3}{10}}\)

\(\large{b)\hspace{1 mm} \frac{17}{10}}\)

\(\large{c)\hspace{1 mm} \frac{197}{1000}}\)

\(\large{d)\hspace{1 mm} \frac{4}{10} = \frac{2}{5}}\)

\(\large{e)\hspace{1 mm} \frac{25}{100} =\frac{5}{20} = \frac{1}{4} }\)

\(\large{f)\hspace{1 mm} \frac{12}{10} = \frac{6}{5}}\)

\(\large{g)\hspace{1 mm} \frac{2555}{100} = \frac{511}{20} }\)

\(\large{h)\hspace{1 mm} \frac{74}{100} = \frac{37}{50} }\)

\(\large{i)\hspace{1 mm} \frac{968}{100} = \frac{484}{50} = \frac{242}{25}}\)

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