Truncation — Definition, Formula & Examples
Truncation is the process of shortening a number by simply removing (dropping) digits past a chosen decimal or place value, without rounding.
Truncation of a real number to decimal places is performed by discarding all digits beyond the -th decimal place, leaving the remaining digits unchanged regardless of the value of the removed digits.
How It Works
To truncate a number, decide how many decimal places (or digits) you want to keep. Then drop every digit after that point. Unlike rounding, you never look at the next digit to decide whether to round up. The kept digits stay exactly as they are. For example, truncating to 2 decimal places means you keep only the first two digits after the decimal point and ignore the rest.
Worked Example
Problem: Truncate 3.84729 to 2 decimal places.
Step 1: Identify the first 2 digits after the decimal point.
Step 2: Drop every digit after the second decimal place. Do not round — just remove them.
Answer: The truncated value is .
Why It Matters
Truncation shows up when calculators or computers store numbers with limited memory — they often truncate rather than round. Understanding the difference helps you judge how much accuracy you lose and avoid small errors that can build up in science, engineering, or financial calculations.
Common Mistakes
Mistake: Confusing truncation with rounding. Students see 3.847 and truncate to 2 decimal places as 3.85 because the third digit (7) is 5 or greater.
Correction: When truncating, you never adjust the last kept digit. You simply remove everything after it. Truncating 3.847 to 2 decimal places gives 3.84, not 3.85.