Quick examples
Select an example to place it in the active input. Each preset demonstrates a different significant-figure rule. Submit the form to inspect each calculation step clearly.
Formula and rules used
Non-zero digits are always significant. Captive zeros between non-zero digits are also significant. Leading zeros only position decimals and never indicate precision.
For multiplication and division, use the fewest significant figures. For addition and subtraction, use the least precise decimal place. Exact counts never restrict precision in measured calculation results.
| Operation | Precision rule | Example |
|---|---|---|
| Count | Count every meaningful measured digit | 0.004560 has 4 significant figures |
| Multiply or divide | Use the fewest significant figures | 10.0 ÷ 3.45 = 2.90 |
| Add or subtract | Use the least precise decimal place | 12.11 + 0.3 = 12.4 |
| Uncertainty | Match the measurement decimal place | 12.35 ± 0.12 |
How to use this calculator
- Select a calculation mode.
- Enter decimal, whole, or scientific notation values.
- Choose rounding, notation, and separator preferences.
- Mark exact numbers when they should not limit precision.
- Calculate, review steps, then copy or export results.
Common significant-figure mistakes
- Counting leading zeros as measured digits.
- Assuming every whole-number trailing zero is significant.
- Using significant-figure rules for addition instead of decimal places.
- Rounding every intermediate value and accumulating avoidable error.
- Reporting uncertainty and measurement with different decimal places.
Calculation history
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Frequently asked questions
What is a significant figure?
A significant figure is a meaningful measurement digit. It communicates measured precision rather than numerical size. More significant digits usually communicate finer reported measurement precision.
Are leading zeros significant?
Leading zeros are not significant. They only position the decimal point. In 0.0045, only the digits four and five count.
Are trailing zeros significant?
Trailing decimal zeros are significant. Whole-number trailing zeros can be ambiguous without notation. Scientific notation clearly communicates every intended precision digit explicitly.
How is zero handled?
A plain zero normally has one significant figure. Written decimal zeros can show additional measured precision. For example, 0.00 communicates exactly two significant measurement figures.
Which rule applies to multiplication?
Use the operand with the fewest significant figures. Calculate first using available precision. Then round the final reported product to appropriate precision.
Which rule applies to addition?
Addition uses decimal-place precision, not significant-figure count. Find the least precise decimal place. Round the final sum to that same decimal place.
What is an exact number?
An exact number comes from counting or a definition. It has unlimited significant figures for calculations. Exact values never reduce precision within measured calculation results.
Why use scientific notation?
Scientific notation removes ambiguity in very large numbers. It also displays precision for very small values. Every written coefficient digit is interpreted as significant automatically.
Should intermediate results be rounded?
Keep guard digits whenever practical during detailed scientific work. This calculator shows each applied operation rule. Final reporting should follow the required precision rule carefully.