Truncating a Number — Definition & Examples

Truncating a Number

A method of approximating a decimal number by dropping all decimal places past a certain point without rounding. For example, 3.14159265... can be truncated to 3.1415.

Note: If 3.14159265...were rounded to the same decimal place, the approximation would be 3.1416.

Worked Example

Problem: Truncate the number 7.86943 to two decimal places.

Step 1: Identify the digit in the second decimal place. The first two decimal places are 8 and 6.

7.\underline{86}943

Step 2: Drop every digit after the second decimal place. Do not look at the remaining digits (943) and do not round.

7.86943 \rightarrow 7.86

Answer: The number 7.86943 truncated to two decimal places is 7.86. (Note: if you had rounded instead, you would get 7.87, because the next digit is 9.)

Why It Matters

Truncation is used in computing and finance where predictable, consistent shortening of decimals is needed. For instance, some computer systems store numbers with a fixed number of digits and simply discard the rest rather than rounding. Understanding the difference between truncating and rounding helps you predict and control the error in your approximations.

Common Mistakes

Mistake: Rounding instead of truncating. For example, truncating 4.678 to one decimal place and writing 4.7.

Correction: When truncating, you never round up. Simply remove the unwanted digits. The correct truncation of 4.678 to one decimal place is 4.6.

Related Terms

Rounding a Number — Alternative approximation method that adjusts the last kept digit
Decimal — The number format truncation is applied to
Significant Digits — Related concept for expressing precision of a number
Approximation — General concept that includes both truncating and rounding