Significant figures calculator
Type 1200 and the count says two; type 1200.0 and it says five. Nothing about the quantity changed — only how you wrote it, and that is precisely what significant figures record. A bare 1200 cannot say whether the hundreds and tens digits were measured or are placeholders, which is the ambiguity scientific notation was invented to remove.
Two separate jobs, and this does both. Counting: 3.14159 has six significant figures, 0.00450 has three, and 1200 has two as written. Rounding: 3.14159 to three significant figures is 3.14. The count row reads the number as a piece of text rather than as a quantity, because that is the only way trailing zeros can mean anything — 1200 and 1200.0 are the same amount and carry different precision.
How to use it
Significant figures are a claim about a measurement, not a property of a number. Writing 2.50 m rather than 2.5 m asserts that you measured to the centimetre and found zero of them, and the whole notation exists so that a calculation cannot quietly invent precision its inputs never had.
Which digits count
Three rules cover every case. Leading zeros never count: they position the decimal point and nothing more, so 0.00450 has three figures, not five or six. Zeros between significant digits always count, so 1002 has four. Trailing zeros count only after a decimal point, which is the rule that does all the work — 1200.0 has five, while a bare 1200 has two as written and might genuinely have been measured to four. That last ambiguity is unfixable in ordinary decimal writing. It is the reason scientific notation exists: 1.2 × 10³ is two figures, 1.200 × 10³ is four, and neither can be misread.
The two arithmetic rules are not the same rule
Multiplication and division carry significant figures: the answer takes the count of the least precise input, so 2.0 × 3.14159 is 6.3 and not 6.28318. Addition and subtraction carry decimal places instead: 12.11 + 0.3 is 12.4, because the second value is only known to one decimal, and its single decimal place caps the sum regardless of how many figures either number has. Applying the multiplication rule to a sum is the most common error in the whole subject, and it produces answers that look more careful than the data behind them. Subtraction of two close values is the case worth watching: 12.345 − 12.344 leaves one significant figure out of five, and no rounding rule can restore what the subtraction destroyed.
Order of magnitude answers a different question
The magnitude row is the power of ten of the leading digit — 0 for 3.14159, −3 for 0.00450, 3 for 4700. It is not a precision measure at all; it is the size of the thing, and it is what you compare when you want to know whether two quantities are in the same league before caring about their digits. Two numbers three orders of magnitude apart differ by a factor of a thousand, and that usually settles an argument faster than any amount of rounding.
What this will not do
It rounds one number to a figure count you choose. It does not propagate significant figures through a calculation, because that requires knowing which operation you performed and in what order, and the rules genuinely differ between the two families above. Enter your final value here and round it once, at the end — rounding intermediate steps is how precision gets lost before the answer is even reached.
What people use it for
- Reporting a lab measurement to the precision the instrument supports
- Checking whether a written figure claims more precision than intended
- Settling how many figures 0.00450 or 1200 actually has
- Rounding a final answer before it goes into a report
- Getting the unambiguous scientific-notation form of a measurement
- Comparing two quantities by order of magnitude rather than by digits
Questions
Three: the 4, the 5 and the trailing zero. The three leading zeros do not count, because they only place the decimal point. Write it as 4.50 × 10⁻³ and the three are the only digits left.
As written, two — and that is genuinely ambiguous rather than a rule being harsh. If all four digits were measured there is no way to say so in plain decimal. Scientific notation settles it: 1.2 × 10³ is two, 1.200 × 10³ is four. Some styles write 1200. with a trailing point to mean four, but it is easy to miss.
The answer takes the significant figures of the least precise input. 2.0 × 3.14159 is 6.3, not 6.28318, because 2.0 only claims two figures and the product cannot claim more than the weakest factor.
No, and this is where most errors come from. Addition and subtraction work on decimal places, not on figures. 12.11 + 0.3 is 12.4, because 0.3 is only known to one decimal place. The number of significant figures in either input is irrelevant to the sum.
Because that is the point. The count reads what you wrote rather than what the value is. 1200 and 1200.0 are the same quantity written with different claims about how well it is known, and only the writing can carry that.
No. Decimal places count rightward from the point; significant figures count from the first non-zero digit wherever it falls. 0.0045678 to two decimal places is 0.00, which throws the number away entirely, while to two significant figures it is 0.0046. For decimal places, use the rounding calculator.
They stop a calculation claiming precision its measurements cannot support. A tape measure good to the millimetre does not become good to the micron because a calculator printed nine digits, and reporting those digits misrepresents the experiment rather than improving it.