Ejercicio resuelto de Física y Química 4 ESO

Usa factores de conversión para los siguientes cambios de unidades de densidad:

a) $\mathrm{13,6}{\text{g/cm}}^3\to \text{kg/L}$
b) $1000{\text{kg/m}}^3\to \text{g/mL}$
c) $\mathrm{4,5}\text{ g/mL}\to \text{mg/L}$
d) $\mathrm{2,75}\text{ cg/cL}\to {\text{hg/m}}^3$
e) $80{\text{mg/cm}}^3\to \text{g/L}$
f) $40\text{ kg/L}\to {\text{g/cm}}^3$
g) $12{\text{mg/mm}}^3\to \text{dg/cL}$
h) $\mathrm{0,9}\text{ g/mL}\to {\text{kg/dm}}^3$
i) $\mathrm{930,5}\text{ mg/L}\to {\text{kg/m}}^3$
j) $14500{\text{kg/m}}^3\to {\text{g/cm}}^3$
k) $\mathrm{0,92}\text{ kg/L}\to {\text{kg/m}}^3$
l) $\mathrm{0,16}\text{ mg/L}\to {\text{kg/m}}^3$

$\mathbf{\text{a)}}$ Un factor para pasar de g a kg y otro de cm³ a L (1 L = 1000 cm³):
$\mathrm{13,6}{\displaystyle \frac{\cancel{\text{g}}}{\cancel{{\text{cm}}^3}}}\cdot {\displaystyle \frac{1\text{ kg}}{1000\cancel{\text{g}}}}\cdot {\displaystyle \frac{1000\cancel{{\text{cm}}^3}}{1\text{ L}}}={\displaystyle \frac{\mathrm{13,6}\cdot 1000}{1000}}{\displaystyle \frac{\text{kg}}{\text{L}}}=\mathrm{13,6}{\displaystyle \frac{\text{kg}}{\text{L}}}$


$\mathbf{\text{b)}}$ Un factor para pasar de kg a g, otro de m³ a L (1 m³ = 1000 L) y otro de L a mL:
$1000{\displaystyle \frac{\cancel{\text{kg}}}{\cancel{{\text{m}}^3}}}\cdot {\displaystyle \frac{1000\text{ g}}{1\cancel{\text{kg}}}}\cdot {\displaystyle \frac{1\cancel{{\text{m}}^3}}{1000\cancel{\text{L}}}}\cdot {\displaystyle \frac{1\cancel{\text{L}}}{1000\text{ mL}}}={\displaystyle \frac{1000\cdot 1000}{1000\cdot 1000}}{\displaystyle \frac{\text{g}}{\text{mL}}}=1{\displaystyle \frac{\text{g}}{\text{mL}}}$


$\mathbf{\text{c)}}$ Un factor para pasar de g a mg y otro de mL a L:
$\mathrm{4,5}{\displaystyle \frac{\cancel{\text{g}}}{\cancel{\text{mL}}}}\cdot {\displaystyle \frac{1000\text{ mg}}{1\cancel{\text{g}}}}\cdot {\displaystyle \frac{1000\cancel{\text{mL}}}{1\text{ L}}}=\mathrm{4,5}\cdot 1000\cdot 1000{\displaystyle \frac{\text{mg}}{\text{L}}}=4500000{\displaystyle \frac{\text{mg}}{\text{L}}}=\mathrm{4,5}\cdot {10}^6{\displaystyle \frac{\text{mg}}{\text{L}}}$


$\mathbf{\text{d)}}$ Un factor para pasar de cg a hg, otro de cL a L y otro de L a m³ (1 m³ = 1000 L):
$\mathrm{2,75}{\displaystyle \frac{\cancel{\text{cg}}}{\cancel{\text{cL}}}}\cdot {\displaystyle \frac{1\text{ hg}}{{10}^4\cancel{\text{cg}}}}\cdot {\displaystyle \frac{100\cancel{\text{cL}}}{1\cancel{\text{L}}}}\cdot {\displaystyle \frac{1000\cancel{\text{L}}}{1{\text{m}}^3}}={\displaystyle \frac{\mathrm{2,75}\cdot 100\cdot 1000}{{10}^4}}{\displaystyle \frac{\text{hg}}{{\text{m}}^3}}=\mathrm{27,5}{\displaystyle \frac{\text{hg}}{{\text{m}}^3}}$


$\mathbf{\text{e)}}$ Un factor para pasar de mg a g y otro de cm³ a L (1 L = 1000 cm³):
$80{\displaystyle \frac{\cancel{\text{mg}}}{\cancel{{\text{cm}}^3}}}\cdot {\displaystyle \frac{1\text{ g}}{1000\cancel{\text{mg}}}}\cdot {\displaystyle \frac{1000\cancel{{\text{cm}}^3}}{1\text{ L}}}={\displaystyle \frac{80\cdot 1000}{1000}}{\displaystyle \frac{\text{g}}{\text{L}}}=80{\displaystyle \frac{\text{g}}{\text{L}}}$


$\mathbf{\text{f)}}$ Un factor para pasar de kg a g y otro de L a cm³ (1 L = 1000 cm³):
$40{\displaystyle \frac{\cancel{\text{kg}}}{\cancel{\text{L}}}}\cdot {\displaystyle \frac{1000\text{ g}}{1\cancel{\text{kg}}}}\cdot {\displaystyle \frac{1\cancel{\text{L}}}{1000{\text{cm}}^3}}={\displaystyle \frac{40\cdot 1000}{1000}}{\displaystyle \frac{\text{g}}{{\text{cm}}^3}}=40{\displaystyle \frac{\text{g}}{{\text{cm}}^3}}$


$\mathbf{\text{g)}}$ Un factor para pasar de mg a dg, otro de mm³ a dm³, otro de dm³ a L (1 L = 1 dm³) y otro de L a cL; el factor de una unidad al cubo se eleva al cubo:
$12{\displaystyle \frac{\cancel{\text{mg}}}{\cancel{{\text{mm}}^3}}}\cdot {\displaystyle \frac{1\text{ dg}}{100\cancel{\text{mg}}}}\cdot {\left({\displaystyle \frac{100\cancel{\text{mm}}}{1\cancel{\text{dm}}}}\right)}^3\cdot {\displaystyle \frac{1\cancel{{\text{dm}}^3}}{1\cancel{\text{L}}}}\cdot {\displaystyle \frac{1\cancel{\text{L}}}{100\text{ cL}}}={\displaystyle \frac{12\cdot {10}^6}{100\cdot 100}}{\displaystyle \frac{\text{dg}}{\text{cL}}}=1200{\displaystyle \frac{\text{dg}}{\text{cL}}}$


$\mathbf{\text{h)}}$ Un factor para pasar de g a kg, otro de mL a L y otro de L a dm³ (1 L = 1 dm³):
$\mathrm{0,9}{\displaystyle \frac{\cancel{\text{g}}}{\cancel{\text{mL}}}}\cdot {\displaystyle \frac{1\text{ kg}}{1000\cancel{\text{g}}}}\cdot {\displaystyle \frac{1000\cancel{\text{mL}}}{1\cancel{\text{L}}}}\cdot {\displaystyle \frac{1\cancel{\text{L}}}{1{\text{dm}}^3}}={\displaystyle \frac{\mathrm{0,9}\cdot 1000}{1000}}{\displaystyle \frac{\text{kg}}{{\text{dm}}^3}}=\mathrm{0,9}{\displaystyle \frac{\text{kg}}{{\text{dm}}^3}}$


$\mathbf{\text{i)}}$ Un factor para pasar de mg a kg y otro de L a m³ (1 m³ = 1000 L):
$\mathrm{930,5}{\displaystyle \frac{\cancel{\text{mg}}}{\cancel{\text{L}}}}\cdot {\displaystyle \frac{1\text{ kg}}{{10}^6\cancel{\text{mg}}}}\cdot {\displaystyle \frac{1000\cancel{\text{L}}}{1{\text{m}}^3}}={\displaystyle \frac{\mathrm{930,5}\cdot 1000}{{10}^6}}{\displaystyle \frac{\text{kg}}{{\text{m}}^3}}=\mathrm{0,9305}{\displaystyle \frac{\text{kg}}{{\text{m}}^3}}$


$\mathbf{\text{j)}}$ Un factor para pasar de kg a g y otro de m³ a cm³; el factor de una unidad al cubo se eleva al cubo:
$14500{\displaystyle \frac{\cancel{\text{kg}}}{\cancel{{\text{m}}^3}}}\cdot {\displaystyle \frac{1000\text{ g}}{1\cancel{\text{kg}}}}\cdot {\left({\displaystyle \frac{1\cancel{\text{m}}}{100\text{ cm}}}\right)}^3={\displaystyle \frac{14500\cdot 1000}{{10}^6}}{\displaystyle \frac{\text{g}}{{\text{cm}}^3}}=\mathrm{14,5}{\displaystyle \frac{\text{g}}{{\text{cm}}^3}}$


$\mathbf{\text{k)}}$ Un factor para pasar de L a m³ (1 m³ = 1000 L):
$\mathrm{0,92}{\displaystyle \frac{\text{kg}}{\cancel{\text{L}}}}\cdot {\displaystyle \frac{1000\cancel{\text{L}}}{1{\text{m}}^3}}=\mathrm{0,92}\cdot 1000{\displaystyle \frac{\text{kg}}{{\text{m}}^3}}=920{\displaystyle \frac{\text{kg}}{{\text{m}}^3}}$


$\mathbf{\text{l)}}$ Un factor para pasar de mg a kg y otro de L a m³ (1 m³ = 1000 L):
$\mathrm{0,16}{\displaystyle \frac{\cancel{\text{mg}}}{\cancel{\text{L}}}}\cdot {\displaystyle \frac{1\text{ kg}}{{10}^6\cancel{\text{mg}}}}\cdot {\displaystyle \frac{1000\cancel{\text{L}}}{1{\text{m}}^3}}={\displaystyle \frac{\mathrm{0,16}\cdot 1000}{{10}^6}}{\displaystyle \frac{\text{kg}}{{\text{m}}^3}}=\mathrm{0,00016}{\displaystyle \frac{\text{kg}}{{\text{m}}^3}}=\mathrm{1,6}\cdot {10}^{-4}{\displaystyle \frac{\text{kg}}{{\text{m}}^3}}$