# What Is A Rounding Error?

When talking about rounding numbers, the ways to do it, and how you can round numbers manually or using a software, you need to keep in mind an important concept – the rounding error.

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## What is A Rounding Error?

Simply put, a rounding error or round-off error is just a mathematical miscalculation that is caused by changing a number to an integer or one with fewer decimals. We can then say that it is mainly the difference between the result of a mathematical algorithm that uses exact arithmetic and that same algorithm that is less precise, or that uses a rounded version of the same number or numbers.

One of the things that you should keep in mind is that the importance or significance of the rounding error varies. In most cases, the rounding error is simply ignored. However, in other cases or circumstances, it may have a cumulative effect. The truth is that a rounding error can be especially problematic when rounded input is used in a series of calculations, causing the error to compound, and sometimes to overpower the calculation.

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## How Does The Rounding Error Works?

Let’s take the case of a rounding error in accounting. If you like the stock market and like to look at financial statements, you may have already seen that some companies keep getting a warning that says that numbers don’t add up due to rounding. In these specific cases, there is no need for rectification. However, some need to be rectified.

Let’s imagine that a financial institution continues to round off interest rates on mortgage loans is a specific month. Now imagine that their customers, based on this rounding, are charged interest rates of 4% and 5% instead of 3.60% and 4.70% respectively.

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In this case, the rounding error could affect tens of thousands of its customers, and the magnitude of the error would result in the institution incurring hundreds of thousands of dollars in expenses to correct the transactions and rectify the error.

With the explosion of big data and related advanced data science applications the possibility of rounding errors has increased dramatically. Many times, a rounding error occurs simply by chance; it’s inherently unpredictable or otherwise difficult to control for. Other times, a rounding error occurs when a researcher unknowingly rounds a variable to a few decimals.

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## The Classic Rounding Error

When talking about the rounding error, it’s impossible not to mention the classic rounding error. Back in 1960, Lorenz, a professor at MIT, input numbers into an early computer program simulating weather patterns. Lorenz changed a single value from .506127 to .506. To his surprise, that tiny alteration drastically transformed the whole pattern his program produced, affecting the accuracy of over two months’ worth of simulated weather patterns.

This helped Lorenz to have a powerful insight to see how things work in the real world: a small, tiny change can have huge consequences. You may have already heard about the “butterfly effect” that was said for the first time after Lorenz suggested that the flap of a butterfly’s wings might ultimately cause a tornado. And the butterfly effect, also known as “sensitive dependence on initial conditions,” has a profound corollary: forecasting the future can be nearly impossible.