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

In physics, we come across a vast range of objects, from quarks, the smallest thing that exists in the universe, to the sun, the largest thing we can see.
It is difficult to get a feel for the largeness or smallness of such objects. To express such quantities, we use the concept of orders of magnitude, or powers of ten method.
Here, all numbers are approximated to the power of ten closest to the given quantity. For example, the radius of the iron nucleus is 4.6 femtometers; this is not the exact value of the radius, but rather just an order of magnitude approximation.
4.6 femtometers can be written as 4.6 times 10 to the power negative 15; so, the radius of the nucleus has an order of magnitude of minus fifteen.
Orders of magnitude helps in making certain assumptions and simplifies calculations.
For instance, when calculating acceleration due to gravity on an object falling from a building, the building height is neglected, as it is few orders of magnitude less than the earth&#39;s radius.

orders of magnitude

Orders of Magnitude

The order of magnitude of a number is the power of 10 that most closely approximates it. Thus, the order of magnitude estimates the scale (or size) of its value. To find the order of magnitude of a number, take the base-10 logarithm of the number and round it to the nearest integer. Then the order of magnitude of the number is simply the resulting power of 10.
The order of magnitude is simply a way of rounding numbers consistently to the nearest power of 10. This makes doing rough mental math with very large and very small numbers easier. For example, the diameter of a hydrogen atom is on the order of 10-10 m, whereas the diameter of the Sun is on the order of 109 m, so it would take roughly 109/10-10 = 1019 hydrogen atoms to stretch across the diameter of the Sun. This is much easier to do in your head than using the more precise values of 1.06&#215;10-10 m for a hydrogen atom diameter and 1.39&#215;109 m for the Sun&#39;s diameter, to find that it would take 1.31&#215;1019 hydrogen atoms to stretch across the Sun&#39;s diameter. In addition to being easier, the rough estimate is also nearly as informative as the precise calculation.

The order of magnitude of a number is the power of 10 that most closely approximates it. Thus, the order of magnitude estimates the scale (or size) of its ...

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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

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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...

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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

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JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

Estimating Scale with Powers of 10

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