Truncate — Definition, Formula & Examples
Truncate means to cut off (or chop off) a number at a specific decimal place, keeping only the digits up to that point and discarding the rest — without rounding.
To truncate a real number to decimal places is to remove all digits beyond the -th decimal place, producing a value no greater in absolute value than the original. Unlike rounding, truncation always moves toward zero (or stays the same) regardless of the discarded digits.
How It Works
Pick the decimal place where you want to truncate. Keep every digit to the left of that cutoff, and simply drop every digit to the right. You never look at the dropped digits to decide whether to round up — you just remove them. For example, truncating to one decimal place gives , even though the next digit is 7. Truncation is sometimes called "rounding down" for positive numbers, but be careful — for negative numbers, truncation moves the value toward zero, not toward negative infinity.
Worked Example
Problem: Truncate 9.6742 to two decimal places.
Identify the cutoff: Two decimal places means you keep the digits through the hundredths place.
Drop the remaining digits: Remove everything after the hundredths digit (the 4 and the 2) without rounding.
Answer: The truncated value is .
Why It Matters
Many calculators and computers truncate values when they run out of display space. In programming, converting a decimal to an integer often truncates rather than rounds, so understanding the difference prevents subtle errors in code and spreadsheets.
Common Mistakes
Mistake: Confusing truncation with rounding. For instance, truncating 4.68 to one decimal place and writing 4.7.
Correction: Truncation never rounds up. You simply drop the extra digits. Truncating 4.68 to one decimal place gives 4.6, not 4.7.