Significant Figures Calculator
Type a number to see how many significant figures it has and why each digit does or does not count. Switch modes to round to any number of significant figures, or to add, subtract, multiply and divide with the sig fig rules applied — all worked on the decimal digits themselves, so 0.1 + 0.2 really is 0.3.
Scientific notation works too: 6.02e23, 6.02 × 10^23 or 6.02×10²³.
Results
4
Significant figures
6
Decimal places
4.050 × 10⁻³
Scientific notation
Digit by digit
| Digit | Place | Significant? | Why |
|---|---|---|---|
| 0 | ones place | No | A leading zero only locates the decimal point. |
| 0 | tenths place | No | A leading zero only locates the decimal point. |
| 0 | hundredths place | No | A leading zero only locates the decimal point. |
| 4 | thousandths place | Yes | Nonzero digits are always significant. |
| 0 | ten-thousandths place | Yes | A zero between nonzero digits is significant. |
| 5 | hundred-thousandths place | Yes | Nonzero digits are always significant. |
| 0 | millionths place | Yes | A trailing zero in a number with a decimal point is significant. |
How to Use the Significant Figures Calculator
- 1. Choose a mode. Count explains the number you type, Round shortens it to the number of significant figures you choose, and Calculate combines two numbers and rounds the answer by the sig fig rules.
- 2. Type the number as you would write it. Trailing zeros matter, so 2.50 and 2.5 are different inputs. Scientific notation can be typed as 6.02e23, 6.02 × 10^23 or 6.02×10²³, and a decimal comma (2,50) is understood.
- 3. Set the options. In Round mode, pick the number of significant figures and what to do with an exact half. In Calculate mode, tick Exact number for anything counted or defined, such as the 2 in 2πr or the 100 in a percentage.
- 4. Read the explanation. Count mode classifies every digit; Round mode names the digit that decided the rounding; Calculate mode shows which number limited the answer and why.
The Rules for Counting Significant Figures
Significant figures are the digits that carry real information about a measurement: every digit you are sure of, plus the first uncertain one. Zeros are the only digits that need rules, because a zero can be a measured value or just a placeholder that locates the decimal point.
| Rule | Example | Significant figures |
|---|---|---|
| Nonzero digits always count | 4.56 | 3 |
| Zeros between nonzero digits count | 1.007 | 4 |
| Leading zeros never count | 0.0045 | 2 |
| Trailing zeros count when there is a decimal point | 2.500 | 4 |
| Trailing zeros in a whole number are ambiguous | 1200 | 2 (up to 4) |
| A trailing decimal point makes them count | 1200. | 4 |
| Every digit of a scientific-notation coefficient counts | 1.20 × 10³ | 3 |
The calculator's default number, 0.004050, uses four of these rules at once. The three leading zeros only place the decimal point; the 4 and the 5 are nonzero; the zero between them is captive; and the final zero follows a decimal point, so someone measured it. That makes 4 significant figures, 6 decimal places, and 4.050 × 10⁻³ in scientific notation.
Exact numbers have unlimited significant figures and never limit an answer. They come from counting (24 students, 3 trials) or from definitions (100 cm in a meter, 2.54 cm in an inch exactly). Mark them as exact in Calculate mode.
Rounding and Calculating With Significant Figures
To round to n significant figures, count n digits from the first nonzero digit, then look at the next one: 5 or more rounds up, less than 5 rounds down. Rounding 2.996 to three significant figures keeps 299, sees a 6, and rounds up to 3.00 — the two zeros are significant and must be written. Rounding 1999 to three gives 2000, which on paper looks like one significant figure, so the calculator recommends 2.00 × 10³ instead.
A remainder of exactly one half is where conventions split. Most textbooks round it up, so 2.45 to two figures is 2.5. Others — and the IEEE 754 standard that computers follow by default — round it to the even digit, giving 2.4, so that halves do not push a long set of results consistently upward. Choose the rule your course uses.
- Multiplication and division: the answer keeps as many significant figures as the measurement with the fewest. 2.5 × 3.42 = 8.55 on a calculator, but 2.5 has only two significant figures, so the answer is 8.6.
- Addition and subtraction: the answer keeps the last decimal place of the least precise measurement. 12.11 + 18.0 = 30.11, but 18.0 is known only to the tenths place, so the answer is 30.1. For whole numbers the same idea applies to tens or hundreds: 1200 + 3.5 rounds to 1200.
Round once, at the end
In a calculation with several steps, keep every digit (or at least one extra guard digit) in the intermediate results and round only the final answer. Rounding at every step lets small errors pile up, and your answer can drift a digit away from the one your teacher's calculator gives.
Common Mistakes
- Dropping significant zeros. A calculator shows 3, but if the answer has three significant figures it must be written 3.00.
- Counting leading zeros. 0.0045 has two significant figures, not four or five.
- Treating 1200 as four significant figures. Without a decimal point or scientific notation, nobody can tell whether the zeros were measured.
- Applying the multiplication rule to a sum. Addition is limited by decimal places, not by the count of significant figures.
- Letting exact numbers limit the answer. The 2 in a diameter formula, d = 2r, has infinitely many significant figures.
Frequently Asked Questions
- How many significant figures does 100 have?
- One, for certain. Without a decimal point its two trailing zeros are ambiguous, and the usual convention is not to count them. Written as 100. it has three significant figures, and as 1.0 × 10² it has two — scientific notation is the clearest way to show exactly which digits were measured.
- Are leading zeros significant?
- No. Leading zeros, such as the three zeros in 0.0045, only show where the decimal point is. Write the number in scientific notation, 4.5 × 10⁻³, and they disappear, which shows they carried no information about the measurement.
- How do significant figures work in scientific notation?
- Every digit of the coefficient is significant and the power of ten is not. 6.02 × 10²³ has three significant figures, and 6.020 × 10²³ has four. This is why scientific notation is the standard way to report a measurement precisely.
- Do exact numbers affect significant figures?
- No. Counted quantities and defined conversion factors are exact and have unlimited significant figures, so they never limit the answer. Only measured values do.
- What is the sig fig rule for addition and subtraction?
- Round the answer to the last decimal place shared by every measurement — the place of the least precise one. 12.11 + 18.0 = 30.11 rounds to 30.1, because 18.0 is only known to the tenths place. The number of significant figures in the answer can be larger or smaller than in the inputs.
- Why does my calculator show 0.30000000000000004?
- Calculators and programs store numbers in binary, where 0.1 and 0.2 cannot be represented exactly, so tiny errors appear in the last place. This tool rounds on the decimal digits you typed, so 0.1 + 0.2 comes out as exactly 0.3.