1.2:
Orders of Magnitude
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's radius.
1.2:
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 1.06×10-10 m for a hydrogen atom diameter and 1.39×109 m for the Sun's diameter, to find that it would take 1.31×1019 hydrogen atoms to stretch across the Sun's diameter. In addition to being easier, the rough estimate is also nearly as informative as the precise calculation.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 1. [Web version]. Retrieved from page 10 https://openstax.org/books/university-physics-volume-1/pages/1-1-the-scope-and-scale-of-physics