What this calculator does
Rounding controls how much precision a number carries. Decimal places fix the digits after the point; significant figures fix the count of meaningful digits regardless of scale. The second is usually the right choice in science and engineering, because it stays consistent whether you are measuring metres or micrometres.
Rounding to a nearest step handles the cases where neither applies: pricing to the nearest five cents, time to the nearest quarter hour, or measurements to the nearest sixteenth. All three modes are shown together, along with floor, ceiling and truncation.
The formula
Rounding to significant figures works by scaling the number so the desired digits sit before the decimal point, rounding there, then scaling back. The scale factor is derived from the order of magnitude, which is why the method works identically for very large and very small values.
| Term | Meaning |
|---|---|
| Decimal places | Digits kept after the decimal point. |
| Significant figures | Meaningful digits counted from the first non-zero one. |
| Floor | Round down to the next whole number. |
| Ceiling | Round up to the next whole number. |
| Truncate | Discard everything after the point, without rounding. |
The inputs explained
| Field | What to enter |
|---|---|
| Number | The number to round. |
| Decimal places | How many digits to keep after the decimal point. |
| Significant figures | How many significant figures to keep, counted from the first non-zero digit. |
| Round to nearest | The step to round to: 0.05 for five-cent pricing, 0.25 for quarter hours, 5 for the nearest five. |
When to use it
Reporting a measurement
Significant figures communicate precision honestly. Writing 12.7 rather than 12.70 says something real about how the measurement was taken.
Pricing to a currency step
Where one and two cent coins have been withdrawn, cash totals round to the nearest five cents. Set the step to 0.05.
Rounding time
Timesheets often round to the nearest quarter hour. A step of 0.25 handles it directly.
Understanding floor and ceiling
Floor always goes down, ceiling always up, regardless of the digit that follows. They matter when the answer must be a whole number of items: you cannot buy 3.2 tins of paint.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Rounding pi to different precisions
The same number rounded to varying numbers of decimal places, with the significant-figure and step results alongside.
| Decimal places | Rounded | To 3 sig figs | Floor · ceiling |
|---|---|---|---|
| 0 | 3 | 3.14 | 3 · 4 |
| 1 | 3.1 | 3.14 | 3 · 4 |
| 2 | 3.14 | 3.14 | 3 · 4 |
| 3 | 3.142 | 3.14 | 3 · 4 |
| 4 | 3.1416 | 3.14 | 3 · 4 |
| 6 | 3.141593 | 3.14 | 3 · 4 |
Significant figures across different magnitudes
The strength of significant figures is that they behave consistently regardless of scale.
| Number | To 3 sig figs | To 2 decimal places |
|---|---|---|
| 0.0004736 | 0.000474 | 0.00 |
| 0.4736 | 0.474 | 0.47 |
| 47.36 | 47.4 | 47.36 |
| 4736 | 4740 | 4736.00 |
| 473600 | 474000 | 473600.00 |
| 47360000 | 47399999.99999999 | 47360000.00 |
Questions
What is the difference between decimal places and significant figures?
Decimal places count digits after the point; significant figures count meaningful digits from the first non-zero one. For 0.004736, two decimal places gives 0.00 while two significant figures gives 0.0047: the second preserves the information.
How do I count significant figures?
Start at the first non-zero digit and count every digit after it, including zeros between digits. Leading zeros never count; trailing zeros after a decimal point do.
What happens with a 5 exactly halfway?
This calculator rounds half away from zero, the convention taught in most schools. Some fields use banker’s rounding, which rounds half to the nearest even digit to avoid accumulating bias across many roundings.
What is the difference between truncating and rounding down?
They are the same for positive numbers. For negatives they differ: truncating −2.7 gives −2, while the floor gives −3, since the floor always moves toward negative infinity.
How many significant figures should I report?
No more than your least precise measurement justifies. Reporting a result to six figures when the inputs were measured to two implies a precision that does not exist.
For very large or small values, see scientific notation. For fractional forms, use the decimal to fraction converter.