Decimal places and significant figures
The two rounding styles answer different questions. Decimal places fix how many digits sit after the decimal point, which is what you want for money and measurements: two decimal places for pounds and pence, one for a temperature. Significant figures fix how many meaningful digits the number keeps in total, counted from the first non-zero digit, which is what science and engineering use because it tracks precision rather than position.
The same number can behave very differently under each rule. 0.004567 to 2 decimal places collapses to 0.00, losing everything, but to 2 significant figures it becomes 0.0046, keeping the precision that matters. Going the other way, 12,345 to any number of decimal places is unchanged, while to 3 significant figures it becomes 12,300.
Worked examples
The halfway rule
When the digit after the cut-off is exactly 5 with nothing behind it, something has to break the tie. This tool uses round half up, the rule taught in UK schools: 2.5 rounds to 3, 3.45 to one decimal place is 3.5, and negative halves round away from zero, so −2.5 becomes −3.
It is worth knowing that another convention exists. Banker's rounding sends halves to the nearest even digit (2.5 becomes 2, 3.5 becomes 4) to stop millions of small round-ups nudging totals upward, and it is the default in Python and in some accounting systems. If a programming language ever gives you a different answer from this page for a value ending in 5, that is almost certainly why.
When rounding goes wrong
Two traps catch people constantly. The first is floating point storage: computers hold decimals in binary, and a number like 2.675 is actually stored a whisker below 2.675, so naive software rounds it to 2.67. This calculator works from the digits you typed and gives the mathematically correct 2.68.
The second is rounding too early. Round only at the final step of a calculation, never in the middle. If you round 1.4 and 1.4 down to 1 each before adding, you get 2 instead of the correct 2.8, and errors like that compound quickly through a long spreadsheet. Keep full precision while you work, then present the result to a sensible number of figures at the end. As a rule of thumb, quote a result to no more significant figures than the least precise number that went into it, and when averaging data one extra decimal place beyond the raw values is plenty. Our mean, median and mode calculator pairs naturally with this one for exactly that job.
Frequently asked questions
What is the difference between decimal places and significant figures?
Decimal places count digits after the decimal point, so 3.14159 to 2 decimal places is 3.14. Significant figures count digits from the first non-zero digit, wherever the decimal point falls, so 0.004567 to 2 significant figures is 0.0046 and 12,345 to 3 significant figures is 12,300.
Which way does a 5 round in this tool?
Up, away from zero. So 2.5 rounds to 3, 3.45 to 1 decimal place is 3.5, and minus 2.5 rounds to minus 3. This is the round half up rule taught in UK schools and used by most calculators and spreadsheets.
Why does 2.675 round to 2.68 here but 2.67 in some software?
Computers store decimals in binary, and 2.675 is actually stored as a value fractionally below 2.675. Naive code sees that lower value and rounds down to 2.67. This tool works from the number you typed, so 2.675 to 2 decimal places correctly gives 2.68.
What is banker's rounding?
A rule where halves round to the nearest even digit, so 2.5 becomes 2 while 3.5 becomes 4. It avoids a small upward bias when summing lots of rounded values, and Python's built-in round function uses it. This tool deliberately does not; halves always round up.
Do zeros count as significant figures?
Leading zeros never do: 0.0046 has 2 significant figures. Zeros between non-zero digits always do: 4,006 has 4. Trailing zeros are significant after a decimal point (2.400 has 4) but ambiguous in a whole number like 1,500, which is one reason scientists prefer standard form.