Las unidades de medida

Aprende y aplica

El sistema internacional de unidades (SI)

El sistema internacional de unidades (SI) está constituido por siete unidades básicas. En este tema nos vamos a centrar en el metro (unidad de longitud) y en las subunidades que se derivan de él.

Longitud, distancia: el metro, múltiplos y submúltiplos.

Será necesario utilizar múltiplos y submúltiplos del metro

El metro es muy útil para medir el ancho, el largo o el alto de clase, pero si queremos medir la distancia entre dos ciudades o la longitud de una goma de borrar, el metro ya no es eficiente.

En cursos anteriores has aprendido cómo pasar de una unidad de medida a sus múltiplos y a sus submúltiplos, así como la relación que hay entre ellos. Vamos a repasar lo que aprendiste. En la siguiente tabla hemos dejado celdas vacías para que las completes. Hemos considerado solamente algunos de los múltiplos y submúltiplos más utilizados:

Tabla de múltiplos:

Prefijo	Símbolo	Factor	Verbalizo
	dam		un decámetro son 10 metros
hecto		10² = 100
	km

Tabla de submúltiplos:

Prefijo	Símbolo	Factor	Verbalizo
	dm	10⁻¹=0,1
			Un metro son 100 centímetros
mili	km

Superficies: metro cuadrado, múltiplos y submúltiplos.

Para medir superficies utilizaremos el metro cuadrado con sus múltiplos y submúltiplos.

También los viste el curso pasado. Haz lo mismo que antes con las tablas siguientes, teniendo en cuenta que son unidades cuadradas y, por tanto, el factor varía:

Tabla de múltiplos:

Prefijo	Símbolo	Factor	Verbalizo
	dam²		Un decámetro cuadrado equivale a 100 metros cuadrados. Es el área de un cuadrado de 10 metros de lado
hecto		10⁴=10 000
	km²

Tabla de submúltiplos:

Prefijo	Símbolo	Factor	Verbalizo
	dm²	10^-2=0,01
			Un metro cuadrado equivale a 10 000 centímetros cuadrados.
mili

Volumen: metro cúbico, múltiplos y submúltiplos.

Vamos a empezar a trabajar también con las unidades de volumen,

Utilizando el metro cúbico, sus múltiplos y submúltiplos. Para medir el espacio que ocupa el aula hemos necesitado medir o estimar tres longitudes. Rellenamos el espacio que ocupa un objeto con cubitos de 1 cm de lado (similar a la siguiente imagen):

Si queremos calcular su volumen no nos sirven las unidades que hemos utilizado para la longitud o la superficie. Necesitamos otras nuevas que vamos a calcular utilizándolas.

El cubo tiene 1 cm de lado. Diremos que su volumen es:

\[V = 1 cm \times 1cm \times 1 cm = 1 cm^3\]

Decíamos antes que medir es comparar lo que quiero medir con un patrón de medida. En este caso, el patrón (unidad) de medida es el cubo de lado 1 cm.

¿Cuántos cubos de 1 cm de arista (lado) caben en el prisma de la izquierda de la imagen de la página anterior?

La respuesta es que caben ___ cubos. Diremos por tanto que el volumen de ese cuerpo es ___ \(cm^3\).

Como la unidad de longitud en el SI es el metro, para el volumen será el metro cúbico.

Un metro cúbico es el volumen que ocupa un cubo de 1 metro de lado.

El volumen tiene tres dimensiones: "largo", "ancho" y “alto”. La unidad base de medida del volumen va a ser el "metro cúbico", escrito m3.

Partimos del metro cúbico.

A partir de esta unidad base obtenemos sus múltiplos y submúltiplos. En la tabla siguiente tienes los más utilizados:

Prefijo	Símbolo	Factor	Verbalizo
deca	\(dam^3 \)	\(10^3=1000 \)	Un decámetro cúbico equivale a \(1000 \) metros cúbicos. Es el volumen de un cubo de 10 metros de lado.
hecto	\( hm^3\)	\(10^6=1\,000\,000 \)	Un hectómetro cúbico equivale a 1 000 000 metros cúbicos. Es el volumen de un cubo de 100 metros de lado.
kilo	\(km^3 \)	\( 10^9=1\,000\,000\,000\)	Un kilómetro cúbico equivale a 1 000 000 000 metros cúbicos. Es el volumen de un cubo de 1 000 metros de lado.

Prefijo	Símbolo	Factor	Verbalizo
deci	\(dm^3 \)	\(10^{-3}=0,001 \)	Un metro cúbico equivale a 1 000 decímetros cúbicos.
centi	\( cm^3\)	\(10^{-6}=0,\,000\,001 \)	Un metro cúbico equivale a 1 000 000 centímetros cúbicos.
mili	\(m^3 \)	\( 10^{-9}=0,\,000\,000\,001\)	Un metro cúbico equivale a 1 000 000 000 milímetros cúbicos.

Aunque no pertenece al SI es muy común utilizar el litro para medir volúmenes, en particular líquidos.

Un litro equivale a 1 decímetro cúbico.

Completa:

Ejercicios

Completa:

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\(2\,km^3=2\cdot\)@@1000000000@@ \(m^3=\,\)@@2000000000@@ \(m^3\)
\(3\,m^3=3\cdot\)@@1000000@@ \(cm^3=\,\)@@3000000@@ \(cm^3\)
\(0,2\,m^3=0,2\cdot\)@@1000@@ \(dm^3=\,\)@@200@@ \(dm^3\)
\(1,32\,hm^3=1,32\cdot\)@@1000000@@ \(m^3=\,\)@@1320000@@ \(m^3\)

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Ejercicios

Completa:

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\(2\,cm^3=2\cdot\)@@0,000001@@ \(m^3=\,\)@@0,000002@@ \(m^3\)
\(3000\,dm^3=3000\cdot\)@@0,001@@ \(m^3=\,\)@@3@@ \(m^3\)
\(301\,mm^3=301\cdot\)@@0,000001@@ \(dm^3=\,\)@@0,000301@@ \(dm^3\)
\(2\,012,3\,m^3=2\,012,3\cdot\)@@0,000001@@ \(hm^3=\,\)@@0,0020123@@ \(hm^3\)

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Ejercicios

Completa:

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\(20\,cl=20\cdot\)@@0,01@@ \(l=\,\)@@0,2@@ \(l\)
\(0,7\,l=0,7\,dm^3=0,7\cdot\)@@1000@@ \(m^3=\,\)@@700@@ \(m^3\)
\(330\,cm^3=330\cdot\)@@0,001@@ \(dm^3=\,\)@@0,33@@ \(dm^3\)
\(0,3\,hm^3=\,\)@@300000@@ \(m^3=\,\)@@300000000@@ \(dm^3=\,\)@@300000000@@ \(l\)

Su navegador no es compatible con esta herramienta.

Otras unidades

No solo existen las unidades que hemos visto en este apartado. En otros países o en otras épocas se usan o se usaban otras unidades como el galón, la pinta o el cántaro.

INVESTIGACIÓN: Busca distintas unidades que se han utilizado o utilizan para medir la capacidad y averigua su equivalencia en litros.

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