Significant Figures Rounder
Round any number to a chosen number of significant figures, or carry them through an expression, shown with trailing zeros kept (2.00) and as a plain value.
You can also type an expression such as 5.13 * 3.78 to combine measurements. Adding and subtracting keeps the fewest decimal places of the terms; multiplying and dividing keeps the fewest significant figures of the factors.
Significant figures in your number: 6
- Significant digits:
314159 - Non-zero digits always count.
3.14
The underlined digit is the last significant one: the precision ends there.
Numeric value: 3.14
Result keeps the zeros that count (2 to 3 figures is 2.00); Numeric value is the same number written plainly, so those zeros drop off (2).
- Start at the first non-zero digit: 3.
- Keep 3 digits from there: 314.
- The next digit is 1, which is less than 5, so the kept digits stay: 314.
- Written out: 3.14.
Which digits carry the precision
Type a number and pick how many significant figures you want, and the result updates live. Type an expression such as 5.13 * 3.78 instead and it is worked out exactly, with the figures carried by the textbook rules — a sum keeps the fewest decimal places of its terms, a product or quotient the fewest significant figures of its factors — and a step-by-step list shows each operation. Significant figures are the digits in a number that carry real meaning about its precision, starting from the first non-zero digit. Rounding 3.14159 to 3 significant figures gives 3.14, and rounding 0.0045678 to 2 significant figures gives 0.0046 — the leading zeros in 0.0045678 are placeholders and do not count. The tool shows two forms of the answer: a formatted string that preserves trailing zeros so the precision is unambiguous (for example 2 rounded to 3 significant figures is shown as 2.00), and the plain numeric value (2) that you would use in further calculations. As you type, it also reports how many significant figures your number already has, reading the count from the number as written so 100 counts as 1, 100. as 3 and 1200.0 as 5, and lists the counting rules that applied to it.
How rounding to significant figures works
To round to n significant figures, you find the first non-zero digit and keep that digit plus the next n−1 digits, rounding the last kept digit based on what follows — a half rounds up, away from zero, unless "Rounding rule" is set to Round half to even. The count ignores leading zeros but includes trailing zeros once they sit after a decimal point, which is why 2.00 and 2 mean different things about how precisely a value is known. In the answer itself the last significant digit is underlined, so 2648 to two figures in plain decimals reads 2600 with the 6 marked and the zeros plainly placeholders. Exact numbers are the exception to all of this: a count, such as the eggs in a carton, or a defined factor, such as 100 cm in a metre, has unlimited significant figures and should never limit an answer. Every number typed here is read as a measurement, so the page says, as soon as you type an expression, to write an exact one with at least as many figures as your most precise measurement, or to leave it out and apply it to the rounded answer. This rounder works on the digits you typed rather than on the nearest binary floating-point value, so 9.995 to 3 significant figures gives 10.0 rather than 9.99, and very large and very small numbers are rounded correctly and may be shown in scientific notation under the Automatic result format (for example 123456 to 3 significant figures becomes 1.23e+5, or 123000); set "Result format" to Plain decimal, Scientific (× 10ⁿ) or E notation to pick the form yourself. To round to a place rather than to a number of figures — the form a sum's answer takes — set “Round to” to Decimal places: the count box becomes a number of decimal places, the digits you typed are rounded by the same rule and padded with zeros to the place, and the result format is set aside.
Frequently asked questions
What counts as a significant figure?
Every digit from the first non-zero digit onward is significant. Leading zeros (as in 0.0046) are only placeholders and are not counted, while trailing zeros after a decimal point (as in 2.00) are significant because they signal measured precision.
Why does the result show trailing zeros like 2.00?
Trailing zeros communicate precision. Rounding 2 to 3 significant figures gives 2.00 to show three meaningful digits. The tool also displays the plain numeric value (2) separately, so you can copy whichever form you need.
Can it do arithmetic with significant figures?
Yes. Type an expression into the Number box — + − × ÷ and ^ with brackets, or * and / — and it is worked out exactly, not in floating point, with nothing rounded until the answer. A sum keeps the fewest decimal places of its terms, a product or quotient the fewest significant figures of its factors, and a power as many as its base. "Significant figures in the answer" says how many that leaves, and "Step by step" lists each operation, its exact value and what that step alone would round to.
What about exact numbers, like counts or unit conversions?
They have unlimited significant figures and should never limit the answer — a count such as the eggs in a carton, or a defined factor such as 100 cm in a metre. This tool reads every number as a measurement, so once you type an expression the page says to write an exact one with at least as many figures as your most precise measurement, or to leave it out and apply it to the rounded answer.
Can it round to decimal places instead of significant figures?
Yes. Set “Round to” to Decimal places and the count box becomes a number of decimal places, with its range in the label; the digits you typed are rounded to that place by the rounding rule you picked and padded with zeros to it, so 2.5 to two places reads 2.50. The result-format choice is greyed out in that mode, since a place is written in plain decimals.