Name: estimating scale with powers of 10
Uploaded: 2023-05-16T08:18:39.000Z
Duration: 1 min 15 s
Channel: JoVE

En física, nos encontramos con una amplia gama de objetos, desde los quarks, la cosa más pequeña que existe en el universo, hasta el sol, la cosa más grande que podemos ver.
Es difícil tener una idea de la grandeza o pequeñez de tales objetos. Para expresar tales cantidades, usamos el concepto de órdenes de magnitud, o el método de potencias de diez.
Aquí, todos los números se aproximan a la potencia de diez más cercana a la cantidad dada. Por ejemplo, el radio del núcleo de hierro es de 4,6 femtómetros; Este no es el valor exacto del radio, sino solo una aproximación de orden de magnitud.
4,6 femtómetros se pueden escribir como 4,6 por 10 elevado a menos 15; por lo tanto, el radio del núcleo tiene un orden de magnitud de menos quince.
Los órdenes de magnitud ayudan a hacer ciertas suposiciones y simplifican los cálculos.
Por ejemplo, al calcular la aceleración debida a la gravedad sobre un objeto que cae de un edificio, se descuida la altura del edificio, ya que es unos pocos órdenes de magnitud menor que el radio de la tierra.

<ol>
	<li>OpenStax. (2019). Física Universitaria Vol. 1. [Versión web]. Recuperado de la página 10 <a href="https://openstax.org/books/university-physics-volume-1/pages/1-1-the-scope-and-scale-of-physics">https://openstax.org/books/university-physics-volume-1/pages/1-1-the-scope-and-scale-of-physics</a></li>
</ol>

orden de magnitud

Orders of Magnitude

La magnitud de un número es la potencia de 10 que más se aproxima a él. Así, el orden de magnitud estima la escala (o tamaño) de su valor. Para encontrar el orden de magnitud de un número, toma el logaritmo en base 10 del número y redúcelo al entero más cercano. Entonces, el orden de magnitud del número sería, simplemente, la potencia resultante de 10. El orden de magnitud es simplemente una forma de redondear números consistentemente a la potencia de 10 más cercana. Esto facilita el cálculo mental aproximado con números muy grandes y muy pequeños. Por ejemplo, el diámetro de un átomo de hidrógeno está en el orden de 10-10 m, mientras que el diámetro del Sol está en el orden de 109 m, por lo que aproximadamente se necesitarían 109/10-10 = 1019 átomos de hidrógeno para abarcar el diámetro del Sol. Esto es mucho más fácil de hacer mentalmente que usar los valores más precisos de 1.06×10-10 m para el diámetro del átomo de hidrógeno y 1.39×109 m para el diámetro del Sol, para encontrar que se necesitarían 1.31×1019 átomos de hidrógeno para abarcar el diámetro del Sol. Además de ser más fácil, la estimación aproximada también es casi tan informativa como el cálculo preciso.

Orden de magnitud

El orden de magnitud de un número es la potencia de 10 que más se aproxima a él. Por lo tanto, el orden de magnitud estima la escala (o tamaño) de su ...

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Unidad 1

Units, Dimensions, and Measurements

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estimating scale with powers of 10

Orders of magnitude help estimate the scale of a number using powers of 10. It is a simple way to round values to the nearest power of 10. This makes it easier to compare very large and very small numbers.

To find the order of magnitude of a number, take its base-10 logarithm and round to the nearest integer. The result gives the power of 10 that most closely matches the original value. This method gives a consistent estimate of size without using exact digits.

Orders of magnitude are useful for rough mental math. For example, the diameter of a hydrogen atom is on the order of 10^-10 m. The diameter of the Sun is on the order of 10^9 m, so about 10^19 hydrogen atoms would stretch across the Sun’s diameter.

That estimate is much easier to work out in your head than the precise values. Using 1.06×10^-10 m for a hydrogen atom and 1.39×10^9 m for the Sun gives 1.31×10^19 atoms. The rough estimate is still nearly as informative as the exact calculation.

Estimating Scale with Powers of 10

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

orders of magnitude

Orders of magnitude help estimate the scale of a number using powers of 10. It is a simple way to round values to the nearest power of 10. This makes it easier to compare very large and very small numbers. To find the order of magnitude of a number, take its base-10 logarithm and round to the nearest integer. The result gives the power of 10 that most closely matches the original value. This method gives a consistent estimate of size without using exact digits. Orders of magnitude are useful...

models, theories, and laws

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units and standards of measurement

SI Units for Physical Quantities

SI units give a standard way to measure physical quantities. A physical quantity can be defined by how it is measured or by how it is calculated from other measurements. For example, the mass and dimensions of a metallic cube can be found with a weighing machine and a meter scale. Some quantities are built from others. The volume of a cube is the cube of its side length. The density of the cube is then found by dividing mass by volume. Measurements are written in units, which are standardized...

estimation of the physical quantities

Fermi Estimation for Physical Quantities

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base quantities and derived quantities

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conversion of units

Unit Conversion Steps and Real-World Errors

Unit conversion lets you change a measurement from one unit to another. It is useful in everyday life, such as when a cookbook gives amounts in liters or ounces and you need cups instead. It also helps when directions use feet or meters, but you want to know the distance in miles. The first step is to list the given unit and the unit you need. The second step is to choose a conversion factor, which is a ratio that shows how many of one unit equal another unit. For example, 1,000 meters equal 1...

accuracy and precision

Repeated Measurements in Science

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random and systematic errors

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rules for significant figures

Measurement Precision and Significant Figures

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significant figures in calculations

Rounding Rules for Significant Figures

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dimensional analysis

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solving problems in physics

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key terms and concepts

Learn how orders of magnitude use powers of 10 to estimate size, compare huge and tiny numbers, and make rough mental math easier.

Estimating Scale with Powers of 10 | JoVE K12

physics

JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

Estimating Scale with Powers of 10

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