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MasterMath

Rounding Calculator

Round a number every way there is: normal, up, down, truncated, banker's rounding, and to any multiple you name.

Rounded

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Rounded—
Truncated—
Rounded up—
Rounded down—
Banker's rounding—
To the given multiple—

How this was worked out

    The rule

    look at the first digit dropped: 5 or more rounds up

    Why it works

    Rounding replaces a number with a nearby simpler one. Which way to go is only genuinely ambiguous at exactly half, and the different rounding rules are precisely different answers to that one question.

    How to do it by hand

    1. Decide how many decimals you want
    2. Look at the first digit being dropped
    3. 5 or more rounds up, less than 5 rounds down
    4. Banker's rounding sends exact halves to the nearest even digit

    What is worth knowing

    Banker's rounding exists because always rounding halves up introduces a systematic upward bias, and over millions of transactions that bias becomes real money. Sending halves to the nearest even digit cancels it out on average, which is why it is the IEEE 754 default and what most financial software uses. Truncating is different from rounding down for negatives: truncating −3.7 gives −3, while rounding down gives −4, and confusing the two is a common source of off-by-one errors in code.

    Frequently asked questions

    What is banker's rounding?

    Exact halves go to the nearest even digit rather than always up. It removes the upward bias of always-up rounding.

    What is the difference between truncating and rounding down?

    For positives, none. For negatives they differ: truncating −3.7 gives −3, rounding down gives −4.

    Why does 0.1 + 0.2 not equal 0.3?

    Because binary floating point cannot represent those decimals exactly. It is a representation issue, not a rounding one.

    When should I round?

    As late as possible. Rounding intermediate results compounds the error through the rest of the calculation.