How to Calculate Order of Magnitude

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Order of magnitude calculations are an important skill to develop. These calculations are a way of estimating specific quantities, which might be difficult (or impossible) to find an exact value for. By making an intelligent estimate, it is possible for you to find a quantity with enough accuracy to be useful for practical purposes, especially if it is sufficient to have a value that is within a certain percentage of the actual value (for instance, 10 percent).

    Identify the quantity you would like to estimate. For example, assume you want to fill a swimming pool using a garden hose, and you would like to know how long this would take. The important quantity here is the amount of time to fill the pool.

    Determine any important intermediate values, which are important for the final estimate. In our example, such quantities include the volume of the swimming pool and the flow rate of the garden hose.

    Identify any calculations that will help you find the intermediate quantities. For example, to find the volume of the swimming pool, you need to know the approximate length, width and depth of the swimming pool.

    Identify anything that relates the intermediate quantities to the desired final quantity. In the example, you can find the time it takes to fill the swimming pool by dividing the volume of the swimming pool by the flow rate of the garden hose.

    Round the answer to the nearest order of magnitude (i.e. the nearest power of 10). For example, assume the time to fill the swimming pool, based on your calculations, is 787,443 seconds. Rounding this to the nearest order of magnitude gives 1,000,000, or 10 to the power of 6. This provides a rough estimate as to how long it would take to fill the swimming pool and shows that the time is closer to 1,000,000 seconds than 100,000 seconds.

    Tips

    • Ensure your estimates are realistic. For example, if you are estimating the weight of a penny, don't assume the weight is 100 pounds.

References

About the Author

Thomas Bourdin began writing professionally in 2010. He writes for various websites, where his interests include science, computers and music. He holds a Bachelor of Science degree in physics with a minor in mathematics from the University of Saskatchewan and a Master of Science in physics from Ryerson University.

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