Significant Figures

General Chemistry • Matter Its Properties and Measurement

Written by STEM Calculators Team Published October 9, 2025 Updated February 24, 2026

Choose a mode. Enter values as plain decimals or scientific notation (e.g., 1.230e3).

Mode

Assume trailing zeros in integers are significant? Example: 1200 has 2 s.f. by default; if checked, it has 4 s.f. (unless written \(1.200\times 10^3\)).

Number Number to round Target s.f. \( N \) Value \( a \) Value \( b \) Operation Value \( p \) Value \( q \) Operation For addition/subtraction, enter plain decimals (no scientific notation) so decimal-place precision is unambiguous.

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Significant Figures

Significant figures (s.f.) indicate the precision of a measured or stated quantity.

Counting rules (vertical examples)

1) Non-zero digits are significant.

\[ \begin{aligned} 1234 &\to 4\ \text{s.f.} \end{aligned} \]

2) Zeros between non-zero digits are significant.

\[ \begin{aligned} 1002 &\to 4\ \text{s.f.} \end{aligned} \]

3) Leading zeros are not significant.

\[ \begin{aligned} 0.004560 &\to 4\ \text{s.f.} \quad (4,5,6,0) \end{aligned} \]

4) Trailing zeros are significant if a decimal point is present.

\[ \begin{aligned} 1.2300 &\to 5\ \text{s.f.} \end{aligned} \]

5) Scientific notation: all digits in the mantissa are significant.

\[ \begin{aligned} 1.230\times 10^{3} &\to 4\ \text{s.f.} \end{aligned} \]

6) Integers without a decimal point: trailing zeros are ambiguous; by default we do not count them (option available).

\[ \begin{aligned} 1200 &\to 2\ \text{s.f.}\ (\text{default}) \\ \text{or } 1200.\ &\to 4\ \text{s.f.} \quad (\text{decimal point marks significance}) \end{aligned} \]

Rounding to \(N\) significant figures

Shift the decimal so the first significant digit is at the ones place, round, then shift back.

\[ \begin{aligned} x &= 0.001995 \\ N &= 3 \\ y &= 0.00200 \quad (\text{3 s.f.}) \\ y &= 2.00\times 10^{-3} \end{aligned} \]

Operations

Multiply / Divide: result has the same number of s.f. as the factor with the fewest s.f.

\[ \begin{aligned} 2.50 \cdot 3.1 &= 7.75 \\ &\to 7.8 \quad (\text{2 s.f.}) \end{aligned} \]

Add / Subtract: result is rounded to the least number of decimal places among the inputs.

\[ \begin{aligned} 12.345 + 0.6 &= 12.945 \\ &\to 12.9 \quad (\text{1 dp}) \end{aligned} \]

Notes

Exact counts and defined constants can be treated as having infinite s.f.
Use scientific notation to make intended precision explicit.
Long expressions should be written vertically for small screens.

Frequently Asked Questions

How do you count significant figures in a number like 0.004560?

Leading zeros are not significant, but nonzero digits are significant and trailing zeros after a decimal point are significant. In 0.004560 the significant digits are 4, 5, 6, and 0, so it has 4 significant figures.

Why are trailing zeros in an integer like 1200 sometimes not counted as significant?

Without a decimal point, trailing zeros in integers can be ambiguous because they may be placeholders rather than measured precision. The calculator lets you choose the convention by toggling whether those trailing zeros are treated as significant.

How does the calculator round results for multiplication and division?

For multiplication or division, the result is rounded to the same number of significant figures as the input with the fewest significant figures. This preserves the measured precision of the least-precise factor.

How does the calculator round results for addition and subtraction?

For addition or subtraction, the result is rounded to the least number of decimal places among the inputs. This is why the add/subtract mode expects plain decimals rather than scientific notation.

Do numbers in scientific notation change the number of significant figures?

Scientific notation makes the intended precision explicit because all digits in the mantissa are significant. For example, 1.230e3 has 4 significant figures because the mantissa 1.230 has four digits of precision.

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