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MasterMath

Truncate Decimals Calculator

Cut a number off after a set number of decimals without rounding, and see how much that differs from rounding it properly.

Truncated

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Truncated—
If it were rounded—
What is discarded—
Do they agree?—

How this was worked out

    The rule

    truncate = drop every digit past the chosen position

    Why it works

    Truncating simply discards the extra digits. Unlike rounding it never looks at what it is throwing away, so it always moves the number towards zero, and it always loses at least as much as rounding would.

    How to do it by hand

    1. Decide how many decimals to keep
    2. Delete everything after that point
    3. Do not adjust the last kept digit
    4. The result is always closer to zero than the original

    What is worth knowing

    Truncation has a systematic bias that rounding does not: it always moves towards zero, so an average of truncated values comes out low. That makes it the wrong choice for money in most contexts, and the right one wherever the convention demands it — tax withholding and interest accrual are often specified as truncated by law, precisely so the result is predictable rather than fair. The distinction matters most with negatives, where truncating and rounding down go opposite ways.

    Frequently asked questions

    What is the difference between truncating and rounding?

    Truncating drops the extra digits without looking at them. Rounding adjusts the last kept digit based on what follows.

    Does truncating introduce bias?

    Yes, always towards zero. An average of truncated values comes out systematically low.

    When is truncation the right choice?

    When a rule or a law specifies it, which is common in tax and interest calculations, where predictability beats fairness.

    What happens with negative numbers?

    Truncating −3.7 gives −3, moving towards zero. Rounding down gives −4, moving away from it.