Significant Figures Calculator
This significant figures calculator rounds a number to however many sig figs you need, or counts the significant figures a number already has. It shows the scientific notation form and flags trailing zeros that could mean two different things.
How to use the significant figures calculator
- Choose a mode: round to N significant figures, or count the sig figs in a number.
- Type the number exactly as it is written, including any trailing zeros.
0.004520and0.00452are different measurements and the calculator treats them that way. - In rounding mode, enter how many significant figures to keep.
- Read the rounded value, the sig fig count and the scientific notation form as they update.
Sig fig and significant figure mean the same thing, and both are used below. If a number has trailing zeros before the decimal point, such as 1200, the count is genuinely ambiguous, and you are told so rather than given a single answer that might be wrong.
The four significant figure rules
Significant figures are the digits in a number that carry real measurement information. Four rules decide which digits count, and there are no exceptions to them.
- Non-zero digits always count. 1 to 9 are significant wherever they appear.
48,923has 5 sig figs. - Captive zeros count. A zero trapped between non-zero digits is always significant.
3.005has 4 sig figs, and90,100has at least 3. - Leading zeros never count. Zeros in front of the first non-zero digit only place the decimal point.
0.00821has 3 sig figs, not 6. - Trailing zeros count only after a decimal point.
5.6900has 5 sig figs, because nobody writes those final zeros unless they measured them. In1200with no decimal point, the trailing zeros are ambiguous.
The reasoning behind the leading zero rule is worth holding on to. In 0.00821 you could change the units — to grams, milligrams, anything — and get 8.21 with no zeros at all. The measurement did not become more or less precise, so those zeros cannot have been carrying information.
Rounding to a set number of sig figs
Count significant digits from the left, starting at the first non-zero digit. Stop when you have as many as you need, look at the next digit, and round up if it is 5 or more. Then keep the place value of everything you dropped by padding with zeros where needed.
Example: 0.004520 to 3 significant figures
The leading zeros are skipped. Counting starts at the 4.
Example: 45,678 to 2 significant figures
Here the padding matters. Cutting the digits without replacing them would turn 45,678 into 46, which is off by a factor of a thousand.
Example: 2.9971 to 3 significant figures
Rounding up carries all the way along, and the resulting zeros must be kept.
That last case trips people up constantly. Writing 3 instead of 3.00 throws away two significant figures and claims far less precision than you have. If you need place-value rounding rather than sig figs — to the nearest hundred, say — the rounding calculator does that instead.
Why 1200 is ambiguous, and how scientific notation fixes it
Write 1200 on paper and there is no way to tell what was measured. It could be a rough figure good to 2 sig figs, a value known to the nearest ten, or an exact count of 1200 items. The digits alone cannot say.
| Intended precision | Scientific notation | Sig figs | Implied range |
|---|---|---|---|
| Nearest hundred | 1.2 × 10³ | 2 | 1150 to 1250 |
| Nearest ten | 1.20 × 10³ | 3 | 1195 to 1205 |
| Nearest unit | 1.200 × 10³ | 4 | 1199.5 to 1200.5 |
Scientific notation removes the doubt because the power of ten handles the size of the number and the digits in front handle nothing but precision. Every digit written before the multiplication sign is significant, so there is no zero left doing double duty.
Two other conventions exist. A trailing decimal point, as in 1200., marks all four digits as significant, though it is easy to miss in print. An overbar or underline on the last significant zero is used in some textbooks. Both are less clear than scientific notation, which is why scientific work uses the latter.
Carrying sig figs through a calculation
An answer cannot be more precise than the measurements it came from. Two different rules apply, and using the wrong one is the most common error in lab reports.
+ and − → match the fewest decimal places
Multiplication and division
Count sig figs in each input and keep the smallest count.
Addition and subtraction
Count decimal places instead. The answer cannot have a digit in a column where one of the inputs had nothing measured at all.
Notice that the addition rule can leave you with more sig figs than either input had: 103.6 has 4, while 0.44 has only 2. That is correct. Adding a small precise number to a large one does not destroy the digits you already knew.
Significant figures reference table
| Number | Sig figs | Why |
|---|---|---|
| 48,923 | 5 | Every digit is non-zero |
| 3.005 | 4 | Captive zeros count |
| 0.00821 | 3 | Leading zeros are placeholders only |
| 0.004520 | 4 | Leading zeros out, final zero after the point in |
| 5.6900 | 5 | Trailing zeros after a decimal point are significant |
| 0.070 | 2 | One leading zero ignored, one trailing zero counted |
| 20.0 | 3 | The decimal point makes both zeros count |
| 1200 | 2, 3 or 4 | Ambiguous — no decimal point to settle it |
| 1.200 × 10³ | 4 | Scientific notation states the precision outright |
| 90,100 | 3, 4 or 5 | Captive zero counts, trailing zeros ambiguous |
| 0.0001 | 1 | Four leading zeros, one measured digit |
Exact numbers are a separate case and have unlimited significant figures. A count of 12 eggs is exactly 12, and a defined conversion such as 1 inch = 2.54 cm is exact by definition. Neither ever limits the precision of an answer.
Common sig fig mistakes
- Confusing sig figs with decimal places. 0.004520 to 3 sig figs is 0.00452; to 3 decimal places it is 0.005. Very different answers.
- Dropping trailing zeros in the answer. 2.9971 to 3 sig figs is 3.00. Writing 3 destroys the precision you were asked to keep.
- Counting leading zeros. 0.00821 has 3 sig figs, not 5 or 6.
- Cutting digits without padding. 45,678 to 2 sig figs is 46,000, not 46.
- Rounding at every step. Round once, on the final answer.
- Using the multiplication rule for addition. Sums and differences follow decimal places, not sig fig counts.
- Applying sig figs to exact counts. A tally of 250 people is exact and does not limit anything.
- Leaving 1200 unqualified in a report. Write it as 1.2 × 10³ or 1.200 × 10³ so the reader knows what you measured. For very large or long numbers where every digit matters, the big number calculator keeps them all exactly.
Frequently asked questions
How many significant figures does 0.004520 have?
Four. The three leading zeros only position the decimal point, so counting starts at the 4. That gives 4, 5, 2 and the final 0, which is significant because it comes after the decimal point and after a non-zero digit. In scientific notation it is 4.520 × 10⁻³, where all four digits are visible.
What is 45,678 to 3 significant figures?
45,700. Keep the first three significant digits, 4, 5 and 6, then look at the next digit, which is 7, so round the 6 up to 7. The remaining columns are filled with zeros to hold the place value. Those two zeros are padding, not significant digits.
Is a sig fig calculator the same as a significant figures calculator?
Yes. Sig fig is just the everyday shorthand for significant figure, and the rules are identical either way. This tool covers both jobs: rounding a number to a given number of sig figs, and counting how many a number already has.
Do zeros count as significant figures?
It depends where they sit. Zeros between non-zero digits always count, so 3.005 has 4. Zeros in front of the first non-zero digit never count, so 0.0082 has 2. Zeros at the end count only if there is a decimal point, so 20.0 has 3 while 200 is ambiguous.
What is the difference between significant figures and decimal places?
Decimal places count digits after the point, no matter what they are. Significant figures count meaningful digits from the first non-zero one, wherever the point falls. Take 0.004520: to 3 sig figs it is 0.00452, but to 3 decimal places it is 0.005. Exam questions specify which they want, so read carefully.
Why is 1200 ambiguous?
Because the trailing zeros could be measured digits or could be placeholders, and written this way there is no way to tell. It might be good to 2, 3 or 4 significant figures. Writing 1.2 × 10³ or 1.200 × 10³ states the precision directly and removes the guesswork.
What is 2.9971 to 3 significant figures?
3.00. The first three significant digits are 2, 9 and 9, and the next digit is 7, so you round up. That carries through both nines and gives 3.00. The two zeros must be written; dropping them to write 3 would claim only one significant figure instead of three.
How many sig figs should my answer have after multiplying?
As many as the input with the fewest. For 3.14 × 2.0, the full product is 6.28, but 2.0 carries only 2 significant figures, so the answer is 6.3. Addition and subtraction use a different rule entirely: match the fewest decimal places rather than the fewest sig figs.
Do exact numbers have significant figures?
They have unlimited significant figures and never limit an answer. Counted quantities are exact, so 24 bottles is exactly 24. Defined conversions are exact too: 1 inch is 2.54 cm by definition, not by measurement. Only measured values constrain the precision of a result.
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