Type the number the way you wrote it in your notebook. This calculator reads the characters instead of a rounded float, so 1.200 counts as four figures and stays four figures.
Plain decimals, negatives, and scientific notation all work. Results update as you type.
Keep every zero you wrote down. They change the answer.
One to fifteen. Past fifteen digits, ordinary measurement stops being the limit and binary storage takes over.
Only changes the answer when the discarded part is an exact half, such as rounding 1.005 to three figures.
Most sig fig tools pass your input to a floating point parser before counting anything. That single step throws away the answer.
Type 1.200 into a parser and you get back 1.2. The two trailing zeros were the whole reason you wrote the number that way, and they are gone before the counting starts. The tool reports two figures. You wrote four.
Rounding breaks in the same place. A parser stores 1.005 as 1.00499999999999989, because binary floating point has no exact form for it. Ask for three figures and you get 1.00. By the half up rule you wrote down in class, the answer is 1.01.
This page walks the characters you typed, applies the counting rule to each one, and rounds with decimal string arithmetic. No parser sits in the middle. What you wrote is what gets counted.
| Example | Figures | Rule at work |
|---|---|---|
| 34.7 | 3 | Non-zero digits always count. |
| 4004 | 4 | Captive zeros sit between non-zero digits, so they count. |
| 0.0052 | 2 | Leading zeros only position the decimal point. |
| 2.500 | 4 | Trailing zeros after a decimal point were measured, so they count. |
| 2500 | 2 to 4 | Trailing zeros in a whole number with no decimal point are unreadable. |
| 6.02e23 | 3 | Exponent digits scale the value. They add no precision. |
| 12 eggs | Unlimited | Counted objects and defined constants have no measurement error. |
The last row trips people up in graded work. A conversion factor like 100 centimetres per metre is a definition, not a reading off an instrument, so it never limits the precision of your answer.
Write 2500 on a lab sheet and you have told your reader almost nothing about your instrument. The value could carry two figures, three, or four. Nothing in the notation says which.
Every fix does the same job. It moves the precision claim somewhere a reader sees it.
2.5 × 103 for two figures, 2.50 × 103 for three. The coefficient states the count with no room for argument. This is the fix to reach for first.2500. marks all four digits as measured. It is compact, though a stray point is easy to miss in handwriting and easy to strip in a spreadsheet.2500 ± 10 skips the convention entirely and reports what you actually know. Journals prefer this over sig figs for exactly that reason.When the input has this problem, the calculator flags it and reports a range instead of pretending to a single number.
Rounding 2.5 to one figure has two defensible answers, and the choice matters more than it looks.
Half up sends every tie upward. It is what most of us learned, and it is fine for a handful of numbers. Across a data set it biases the total, because ties always move one direction and never the other.
Half to even sends the tie to whichever neighbour leaves an even last digit, so 2.5 becomes 2 and 3.5 becomes 4. Ties split roughly evenly between up and down, and the bias in a long column of numbers cancels out. It is the IEEE 754 default, which means your spreadsheet, your Python session, and most lab instruments already do this.
Set the toggle to match whoever grades or reviews your work. If nobody has told you, half to even is the safer habit for anything you plan to sum.
Counting one number is the easy half. Combining measurements has its own rules, and they differ by operation.
4.56 × 1.4 gives 6.4, held to two figures by the 1.4.12.11 + 0.3 gives 12.4, held to one decimal place by the 0.3.Subtraction of two close numbers deserves a second look. Take 8.324 − 8.319. Both inputs carry four figures, the difference is 0.005, and only one figure survives. Nothing went wrong in the arithmetic. The precision was consumed by the digits the two values had in common, which is why analytical methods avoid subtracting large near-equal quantities where they can.
Worth knowing before you rely on it for graded or published work.
Two common reasons. Most tools parse your input as a floating point number first, which deletes trailing zeros and shifts exact halves like 1.005 slightly below the tie. This page counts the characters you typed and rounds with decimal arithmetic, so those two failure modes do not apply. The other reason is the tie-breaking rule, since half up and half to even give different answers at an exact half.
Three. The leading zeros only position the decimal point, so counting starts at the 4. The final zero sits after a decimal point, which marks it as measured rather than as a placeholder. Digits 4, 5, and 0 all count.
Not from the notation alone. In 4500 the two zeros could be measured or could be filling space to the decimal point, and no rule settles it. Rewrite the value in scientific notation, add a trailing decimal point, or state the uncertainty. This calculator reports a range for numbers written that way.
Only the ones in the coefficient. In 1.20 x 10^4 the count is three, taken from 1.20. The exponent scales the value and never contributes figures. This is why scientific notation removes the trailing zero ambiguity, since every digit you write in the coefficient is a claim about precision.
Precision is how finely you resolved a value, which is what significant figures describe. Accuracy is how close that value sits to the truth. A miscalibrated balance reading 12.4783 g is precise to six figures and still wrong. Sig figs make no claim about accuracy at all.
No. Rounding early compounds error through the chain. Carry two extra guard digits through intermediate steps, then round once at the end using the rule that fits the final operation, figure count for multiplication and division, decimal places for addition and subtraction.
