How do I know how many significant figures a number has?

First, ignore any leading zeros. Then count all remaining digits, including zeros between non-zero digits. For numbers with a decimal point, trailing zeros to the right of the last non-zero digit are significant. For whole numbers without a decimal point, trailing zeros are often considered ambiguous and may or may not be significant depending on the measurement context or notation used.

How do I round a number to a given number of significant figures?

Identify the digit corresponding to the desired number of significant figures, then look at the next digit to the right. If that next digit is 5 or greater, round the last kept digit up; if it is less than 5, keep the last digit unchanged. Adjust the decimal point and use scientific notation when necessary to keep the correct number of significant digits.

What are the rules for significant figures in multiplication and division?

For multiplication and division, the result should be reported with the same number of significant figures as the factor with the fewest significant figures. For example, if you multiply 2.51 (three significant figures) by 3.2 (two significant figures), the product should be reported with two significant figures.

What are the rules for significant figures in addition and subtraction?

For addition and subtraction, the limiting factor is the number of decimal places, not the count of significant figures. The result should be rounded so that it has no more decimal places than the term with the fewest decimal places. For example, 12.11 + 3.4 should be reported as 15.5, because 3.4 has one decimal place.

How reliable is this significant figures calculator?

The calculator implements the standard significant figure rules used in most introductory science and engineering courses and follows widely accepted conventions. It handles decimal and scientific notation, counts significant digits, and applies rounding rules consistently. As with any tool, you should still use professional judgement and, for formal laboratory reports or regulatory submissions, follow the conventions required by your institution or standards body.

Significant Figures Calculator

Q: What are significant figures?

Significant figures are the digits in a measured or calculated quantity that carry meaningful information about its precision. They include all non-zero digits, zeros between non-zero digits, and in many conventions, trailing zeros in numbers with a decimal point. They are used in physics, chemistry, and engineering to communicate how precisely a quantity is known.

Precision & rounding helper

Count significant figures, round to a given number of significant digits, and apply sig-fig rules to multiplication, division, addition and subtraction. Designed for physics, chemistry and engineering practice where communicating uncertainty and precision really matters.

counts sig figs round to N sig figs × / ÷ sig fig rule + / − decimal rule scientific notation

Interactive significant figures calculator

Mode

Choose whether you want to count sig figs in a number, round a value to a specified number of significant digits, or apply sig-fig rules to arithmetic operations.

Count significant figures

Value

You can use decimal point (.), scientific notation (1.23e4 or 1.23×10^4) and optional leading/trailing zeros. The calculator assumes standard intro-chem/physics conventions.

What are significant figures?

Significant figures (or sig figs) are the digits in a number that carry meaningful information about its precision. In measurements, they reflect the smallest scale of the instrument and the care taken in recording the value. In calculations, they help prevent reporting an unrealistic number of digits.

Core rules for counting significant figures

1. Non-zero digits are always significant

\(1, 2, 3, \dots, 9\) are always counted.
\(124.7\) has 4 significant figures.
\(6.02\) has 3 significant figures.

2. Leading zeros are not significant

Zeros that appear before the first non-zero digit only locate the decimal point.

\(0.0045\) has 2 significant figures (4 and 5).
\(0.000\,120\) has 3 significant figures (1, 2 and the trailing zero after the 2, because of the decimal).

3. Zeros between non-zero digits are significant

Any zero sandwiched between two non-zero digits counts.

\(1003\) has 4 significant figures.
\(3.0709\) has 5 significant figures.

4. Trailing zeros with a decimal point are significant

If a number has a decimal point, zeros to the right of the last non-zero digit are significant. They show that the measurement was recorded to that level of precision.

\(12.0\) has 3 significant figures.
\(0.0400\) has 3 significant figures.
\(100.\) has 3 significant figures (the decimal point indicates the zeros are measured, not placeholders).

5. Trailing zeros without a decimal point are ambiguous

In a whole number with no decimal point, trailing zeros may or may not be significant depending on context. Many teaching conventions assume they are not significant unless explicitly indicated.

\(1500\) is often treated as having 2 significant figures (1 and 5) by default.
To show 3 significant figures, write \(1.50 \times 10^3\).
To show 4 significant figures, write \(1.500 \times 10^3\).

This calculator reports the conventional minimum sig figs for such integers and flags them as “ambiguous” so you know context might matter.

Rounding to a given number of significant figures

To round a value to \(N\) significant figures:

Identify the first non-zero digit; counting starts there.
Count digits from left to right until you reach the \(N\)-th digit.
Look at the next digit to the right:
- If it is 5 or greater, round the \(N\)-th digit up.
- If it is less than 5, leave the \(N\)-th digit as it is.
Replace any remaining digits with zeros (for whole numbers) or drop them (for decimals) as appropriate.
Use scientific notation if necessary to keep the number readable.

Example 1 – rounding a large number

Round \(12345\) to 3 significant figures:

Digits: 1 (1st), 2 (2nd), 3 (3rd), 4 (next), 5.
The 3rd digit is 3; the next digit is 4 (less than 5).
Result: \(12300\) (3 significant figures).

Example 2 – rounding a small decimal

Round \(0.004567\) to 2 significant figures:

Skip leading zeros → first non-zero is 4 (1st sig fig), then 5 (2nd sig fig), next digit is 6.
6 ≥ 5, so round the 5 up to 6.
Result: \(0.0046\) (2 significant figures).

Significant figures in calculations

Multiplication and division

For products and quotients, the result should have the same number of significant figures as the factor with the fewest significant figures.

Example: \(2.51 \times 3.2\)
\(2.51\) → 3 sig figs, \(3.2\) → 2 sig figs.
Raw product: \(2.51 \times 3.2 = 8.032\).
Rounded result (2 sig figs): \(8.0\).

Addition and subtraction

For sums and differences, the result should have the same number of decimal places as the term with the fewest decimal places.

Example: \(12.11 + 3.4\)
\(12.11\) has 2 decimal places, \(3.4\) has 1 decimal place.
Raw sum: \(15.51\).
Rounded result (1 decimal place): \(15.5\).

Scientific notation and significant figures

Scientific notation is ideal when you want to state significant figures unambiguously. In a number written as \(a \times 10^n\), all digits in the coefficient \(a\) are significant.

\(6.02 \times 10^{23}\) has 3 significant figures.
\(1.500 \times 10^3\) has 4 significant figures.
\(4.0 \times 10^{-2}\) has 2 significant figures.

Worked examples with the calculator

Example – count sig figs in 0.0400

Enter 0.0400 in “Count significant figures”.
The tool reports 3 significant figures (4, 0, 0) and explains that trailing zeros in a decimal are significant.

Example – multiply with sig-fig rule

Select “Operations with significant figures → Multiplication / Division”.
Value A = 2.51, Value B = 3.2.
The tool computes the raw product 8.032, counts sig figs (3 and 2), and reports the rounded result 8.0 with 2 significant figures.

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