Significant Figures Calculator

Significant figures are the digits in a measurement that carry real information. Read the number left to right and apply four rules:

1. Every non-zero digit counts. $47.3$ has 3.
2. Zeros between non-zero digits count. $2005$ has 4.
3. Leading zeros never count. They only place the decimal point, so $0.0042$ has 2 sig figs, not 4.
4. Trailing zeros count only if there is a decimal point. $0.004070$ has 4; $2.500$ has 4; but $4500$ written with no decimal point has an ambiguous 2.

The idea behind rule 3 is that $0.0042$ and $4.2 \times 10^{-3}$ are the same measurement written two ways, and nobody thinks $4.2$ has four digits of precision. The idea behind rule 4 is the opposite: writing the final zero in $2.500$ is a deliberate claim that you measured that far.

1. Count from the first significant digit, not from the decimal point. In $0.0027495$ the first significant digit is the $2$.
2. Mark the last digit you are keeping. For 3 sig figs that is $2,\, 7,\, 4$.
3. Look at the very next digit only. If it is 5 or more, round the kept digit up; otherwise leave it.
4. Refill the place value with zeros so the number keeps its size.

So $0.0027495$ to 3 sig figs is $0.00275$ — the next digit was a $9$, so the $4$ became a $5$.

The place-value refill is where answers go wrong. Rounding $48\,721$ to 2 sig figs gives $49\,000$, not $49$. You must keep the zeros, otherwise you have changed the number by a factor of a thousand.

Multiplication and division — count sig figs. The answer gets the same number of significant figures as the input that has the fewest. $4.56 \times 1.4 = 6.384$, but $1.4$ has only 2 sig figs, so the answer is $6.4$.

Addition and subtraction — count decimal places. The answer gets the same number of decimal places as the input with the fewest. $12.11 + 18.0 = 30.11$, but $18.0$ has only one decimal place, so the answer is $30.1$.

The mistake almost everyone makes is using the multiplication rule on a sum. In $100.0 + 0.234$, the $0.234$ has 3 sig figs, but it does not force the answer to 3 sig figs — the answer is $100.2$, which has 4. Precision in a sum is limited by where the uncertainty sits, not by how many digits you wrote.

Also: do not round between steps. Carry the full calculator value through and round once at the end, keeping a note of how many figures each step is entitled to.