## What is a 'Rounding Error'

A rounding error is a mathematical miscalculation caused by altering a number to an integer or one with fewer decimals. The significance of rounding error depends on the circumstances. While it is inconsequential enough to be ignored in most cases, rounding error can have a cumulative effect in the present-day computerized financial environment, in which case it may need to be rectified.

The term "rounding error" is also used sometimes to indicate an amount that is not material to a very large company.

Next Up

## BREAKING DOWN 'Rounding Error'

Financial statements of many companies routinely carry the warning that "numbers may not add up due to rounding." In such cases, the apparent error is only caused by the financial spreadsheet's quirks, and would not need rectification.

## Example of a Rounding Error

For example, consider a situation where a financial institution mistakenly rounds off interest rates on mortgage loans in a given month, resulting in its customers being charged interest rates of 4% and 5% instead of 3.60% and 4.70% respectively. 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.

The explosion of big data and related advanced data science applications has only amplified the possibility of rounding errors. Many times a rounding error occurs simply by chance; it's inherently unpredictable or otherwise difficult to control for — hence, the many issues of "clean-data" from big data. Other times, a rounding error occurs when a researcher unknowingly rounds a variable to few decimals.

The classic rounding error exemplar includes the story of Edward Lorenz. Around 1960, Lorenz, a professor at MIT, input numbers into an early computer program simulating weather patterns. By changing a single value from .506127 to .506 — to his surprise, that tiny alteration drastically transformed the whole pattern his program produced, over two months of simulated weather.

The unexpected result led Lorenz to a powerful insight into the way nature works: small changes can have large consequences. The idea came to be known as the “butterfly effect” 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. Today, a more elegant form of the butterfly effect is known as chaos theory. Further extensions of these effects are recognized in Benoit Mandelbrot's research into fractals and the "randomness" of financial markets.

RELATED TERMS
1. ### Accounting Error

An accounting error is an error in an accounting entry that was ...
2. ### Transposition Error

Transposition error is a simple error of data entry which occurs ...
3. ### Non-Sampling Error

A non-sampling error is an error that results during data collection, ...
4. ### Rounding Top

A rounding top is a chart pattern used in technical analysis ...
5. ### Fat Finger Error

A fat finger error is a human error caused by pressing the wrong ...
6. ### Sampling Error

A sampling error is a statistical error that occurs when an analyst ...
Related Articles

### 3 Costly Spelling Errors

History has proved that some spelling errors can cost companies and governments millions of dollars.
2. Investing

Human beings often act irrationally when it comes to business decisions. Behavioral finance explains the difference between what we should do and what we do.

### What is an Iron Butterfly Option Strategy?

The iron butterfly options play can generate profits for market players who believe there will be minimal price movement until expiration.
4. Investing

Chances are your credit report has mistakes – which could cost you hundreds a year in mortgage, car loan or credit card interest. Here's how to correct it.
5. Taxes

### Seven Deadly Sins to Avoid During Tax Season

Make sure your tax return is error-free before filing with these seven tips.
6. Investing

Facebook risks irking its important advertising customers after disclosing its tenth error since September 2016.
7. Retirement

### Important Changes If You Miss a IRA or Other Rollover Deadline

A non-qualified distribution might still be tax and/or penalty free under certain conditions.
8. Insights

### Stanford Study Says Fitness Trackers Can't Count Calories

Researchers say those relying on fitness trackers to measure their calorie expenditure are being misled.
RELATED FAQS
1. ### Is tracking error a significant measure for determining ex-post risk?

Before we answer your question, let's first define tracking error and ex-post risk. Tracking error refers to the amount by ... Read Answer >>
2. ### How do I calculate the standard error using Matlab?

Learn how to calculate the standard error for a sample statistical measure, such as the sample mean, using standard Matlab ... Read Answer >>
3. ### What affects your credit score

Learn how your checking account relates to your credit score, as well as what types of banking activities do and do not get ... Read Answer >>
4. ### What are some examples of inherent risk?

Defining the nature of inherent risk in preparing and executing financial audits, and explaining its prevalence in the financial ... Read Answer >>
Hot Definitions
1. ### Portfolio

A portfolio is a grouping of financial assets such as stocks, bonds and cash equivalents, also their mutual, exchange-traded ...
2. ### Gross Profit

Gross profit is the profit a company makes after deducting the costs of making and selling its products, or the costs of ...
3. ### Diversification

Diversification is the strategy of investing in a variety of securities in order to lower the risk involved with putting ...
4. ### Intrinsic Value

Intrinsic value is the perceived or calculated value of a company, including tangible and intangible factors, and may differ ...
5. ### Current Assets

Current assets is a balance sheet item that represents the value of all assets that can reasonably expected to be converted ...
6. ### Volatility

Volatility measures how much the price of a security, derivative, or index fluctuates.