How many figures does 1200 have?

Genuinely unclear, and this tool counts two - the common convention when nothing marks the zeros as measured. If you know the value is precise to four figures, write it as 1.200 × 10³ and the ambiguity disappears. This is not a shortcoming of the tool but of decimal notation, which has no way to distinguish a placeholder zero from a measured one.

Do counted things follow these rules?

No, and this matters. Twelve eggs is exactly twelve, with no uncertainty at all, so it never limits the precision of an answer. The same goes for defined constants: twelve inches in a foot is exact by definition. Only measured quantities carry uncertainty, and only they should be counted when deciding how to round.

When should I round - at the end or as I go?

Carry the full precision through every intermediate step and round only the final answer. Rounding at each stage lets small errors accumulate, and in a long calculation they can move the last digit or two. This tool shows the unrounded value alongside the rounded one for exactly that reason: the unrounded figure is what you feed into the next step.

How does this differ from the scientific notation page?

That page changes how a number is written; this one changes how many digits it keeps and what a calculation is allowed to claim. They meet at one point - scientific notation makes a figure count unambiguous - but rounding to three figures and rewriting as a power of ten are different operations answering different needs.

Significant Figures Calculator - Count, Round and Calculate

2on / / Calculators / Math Calculators / Significant Figures

Significant figures

Count and round

Number

Round to how many figures

Combine two measurements

Operation

The digits that carry information

A measurement carries its own uncertainty in how it is written. A ruler marked in millimetres gives 12.4 cm, not 12.4000 cm, and writing the extra zeros would claim a precision the ruler never had. Significant figures are the convention that keeps that claim honest: they say which digits were actually measured and which are just the arithmetic running on afterwards.

Using it in three steps

1 Type a number to see how many significant figures it carries.
2 Set the figure count to round it, if that is what you came for.
3 For a calculation, enter both measurements below and the correct rule is applied for you.

Which zeros count and which do not

Zeros are the whole difficulty. Leading zeros never count - 0.0042 has two significant figures, because those zeros only place the decimal point. Zeros between digits always count: 1002 has four. Trailing zeros after a decimal point count, so 1.200 has four and says the measurement was good to a thousandth. Trailing zeros in a whole number like 1200 are genuinely ambiguous, and scientific notation exists partly to settle that argument.

Why the two rules are different

Multiplying stretches relative error, so the answer inherits the weakest relative precision - counted in significant figures. Adding stretches absolute error, so the answer inherits the weakest absolute precision - counted in decimal places. That is the whole reason the two rules differ, and it is why 2.0 × 3.000 is 6.0 while 2.0 + 3.000 is 5.0: same inputs, different question, different weakest link.

Significant figures - frequently asked questions

Because the extra zeros are a claim, not decoration. Writing 1.200 states that the measurement was taken to the nearest thousandth and came out at zero there; writing 1.2 says only that it was between 1.15 and 1.25. The two numbers are equal in value and different in what they promise, which is exactly the distinction significant figures exist to record.

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