# Rounding Error

## What it is:

A** rounding error **is a mistake made when rounding a number up or down.

## How it works (Example):

For example, most math books teach students to round numbers 5 through 9 up. For example, the number 10.5693 would round up to 11. Similarly, the number 4.48753 would round down to 4. A rounding error could occur if an analyst accidentally rounds 10.5693 down to 10 instead of up to 11.

Rounding errors often become obvious in percentages. For example, if we have three types of cost to make a widget, and we want to see which cost is the largest portion of the total cost, we might have the following list:

Cost A: 4.567%

Cost B: 85.654%

Cost C: 9.779%

Total: 100.000%

If we round those percentages to the nearest whole number, we get:

Cost A: 5%

Cost B: 86%

Cost C: 10%

Total: 101%

As you can see, the total is 101%, which isn't mathematically possible. The difference is due to rounding. Whether this is an "error" is a matter of opinion (the numbers were rounded correctly, but the total doesn't add due to rounding), but the important point is that rounding is an important consideration, especially when using large volumes of data.

## Why it Matters:

Rounding errors can make significant differences in analyses and the decisions that come from them. For example, if 10.5693 had represented the number of cases of parts necessary to fill a customer order, or the estimated value of a company's shares, or the number of employees necessary to operate a factory section, then a rounding error could have disastrous consequences. Most spreadsheets automatically round things correctly, but one should be cautious when doing calculations by hand or evaluating estimates provided by others.