Mathematics, Statistics & Geometry

Significant Figures Calculator

Round any number to a specified number of significant figures. See the exact rounding method, scientific notation, and step-by-step workings.

Rounded to 3 Sig. Fig.
3.14
Scientific Notation3.14 × 10^0
Original Sig. Figures (est.)9
Rounding Factor1 / 100
Calculation StepsRound 3.14159265 to 3 significant figure(s) Step 1: Magnitude = floor(log₁₀(|3.14159265|)) = floor(0.4971) = 0 Step 2: Rounding factor = 10^(3 - 1 - 0) = 10^2 = 100 Step 3: Round(3.14159265 × 100) / 100 = Round(314.159265) / 100 Step 4: Result = 3.14

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Precision in Measurement

The Significant Figures calculator helps you maintain mathematical integrity by rounding numbers to the correct level of precision. Whether you are performing a lab experiment or engineering a part, knowing how many "sig figs" to keep is vital for accurate reporting.

Rounded Value=round(x,sigFigs)\begin{aligned} \text{Rounded Value} = \text{round}(x, sigFigs) \end{aligned}

Where:
x=
The number to be rounded
sigFigs=
The number of significant digits to retain

Rules for Identifying Significant Figures

  1. All non-zero digits are always significant (e.g., 123 has 3).
  2. Zeros between non-zero digits are significant (e.g., 102 has 3).
  3. Leading zeros are NEVER significant (e.g., 0.002 has 1).
  4. Trailing zeros with a decimal ARE significant (e.g., 45.0 has 3).
  5. Trailing zeros without a decimal are ambiguous (e.g., 4500 is usually 2).

The Importance of Scientific Notation

To remove ambiguity from trailing zeros, scientists use scientific notation.

  • 4.5 × 10³ clearly indicates 2 significant figures.
  • 4.500 × 10³ clearly indicates 4 significant figures.

Rounding Rules

When rounding to sig figs, we follow standard rounding conventions. If the first digit to be dropped is 5 or greater, round up the last significant digit. If it is less than 5, leave it unchanged. Our calculator handles this logic automatically for any number of digits.

Frequently Asked Questions

Significant figures are the digits in a number that carry meaning contributing to its measurement resolution. They include all non-zero digits, zeros between non-zero digits, and trailing zeros in a decimal.

No. Leading zeros (zeros at the beginning of a decimal, like 0.005) are not significant. They are placeholders used to indicate the scale of the number.

Trailing zeros are significant if there is a decimal point present (e.g., 5.00 has 3 sig figs). If there is no decimal point (e.g., 500), the zeros are usually considered ambiguous but often treated as non-significant placeholders.

Identify the first non-zero digit. Count the required number of digits from there. Look at the next digit to decide whether to round up (5 or higher) or stay the same (4 or lower).

They communicate the precision of a measurement. You cannot have a result more precise than your least precise measurement. Sig figs prevent 'false precision' in calculations.

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