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Significant Figures Calculator

Free significant figures calculator — count the sig figs in any number and round it to a chosen number of significant figures.

Number, exactly as writtenHow it is written matters — 1500, 1500. and 1.5e3 carry different precision claims.Round to (significant figures)

0.00340

Leading zero — a placeholder only
Significant
Trailing zero after a decimal point — counts

3 significant figures

Each digit is coloured by why it does or does not count.

Significant figures

Rounded to 3 s.f.

0.003

Scientific notation

3.40 × 10⁻³

Value

0.003

Digits that count3

Leading zeros (never count)3

Zeros between significant digits0

Trailing zeros after a decimal point1

Ambiguous trailing zeros0

Instant insight

0.00340 has 3 significant figures
Every non-zero digit counts. Zeros between significant digits count. Leading zeros never do — they only place the decimal point. Trailing zeros after a decimal point do, because the writer went to the trouble of writing them.
The 3 leading zeros are not significant
0.00340 has three significant figures, not five. Leading zeros carry no information about precision — they only say where the decimal point sits, and writing the same quantity as 3.40 × 10⁻³ removes them entirely without changing anything about the measurement.
Scientific notation states the precision explicitly
Written as 3.40 × 10^-3, the number of digits in the mantissa IS the number of significant figures — no rules to apply, no ambiguity to resolve. That is why scientific work uses it: it carries the precision in its form rather than relying on a convention the reader has to know.
Rounded to 3 significant figures: 0.003
Rounding to a given number of significant figures is not the same as rounding to a number of decimal places: the first tracks precision relative to the size of the number, the second is absolute.
The two arithmetic rules are different, and easy to mix up
Multiplying or dividing: the answer carries the fewest significant figures of any input. Adding or subtracting: it carries the fewest DECIMAL PLACES. Those are not the same rule. 100.0 + 0.001 has four significant figures in each input, and the answer keeps one decimal place — 100.0, not 100.001.
What significant figures do and do not tell you
They record how precisely something was measured, not how accurate it is. A badly calibrated instrument can report six significant figures of a wrong value. Precision is repeatability; accuracy is closeness to the truth, and the digits can only speak to the first.

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Everyday Uses

Reporting to justified precision

Report a calculated result to the precision your instruments actually justified.

Measurement work

Combine measurements of differing precision without overstating the answer.

Chemistry and physics problems

Apply the right rule — significant figures for products, decimal places for sums.

Engineering tolerances

Keep stated precision consistent with what can be measured and manufactured.

Do not out-claim your instrument

A ruler marked in millimetres cannot justify an answer to four decimal places, whatever the calculator display offers. The figures you report are a statement about your equipment.

Two different rules

Multiplication and division keep the fewest significant figures; addition and subtraction keep the fewest decimal places. Applying the wrong one is the most common slip in lab work.

Frequently Asked Questions

Which digits are significant?

All non-zero digits count. Zeros between non-zero digits count. Leading zeros never count — 0.0043 has two significant figures. Trailing zeros after a decimal point do count, because writing them is a claim about precision: 4.30 has three. Trailing zeros in a whole number are ambiguous, which is precisely why 4,500 is unclear and 4.5 × 10³ is not.

Why do significant figures matter?

Because they communicate how precise a measurement actually is, and stop calculations manufacturing precision that was never measured. If you measure a room as 3.2 by 4.1 metres, the product is 13.12 on a calculator — but reporting 13.12 claims accuracy to a hundredth of a square metre from measurements accurate to a tenth of a metre. The honest answer is 13 square metres.

What are the rules for calculations?

Two different rules, which is the part people miss. For multiplication and division, the result takes the same number of significant figures as the least precise input. For addition and subtraction, it takes the same number of decimal places as the input with the fewest — not significant figures, decimal places. Applying the multiplication rule to a sum is a very common mistake.

When should I round — during or at the end?

At the end. Rounding intermediate steps compounds error through the calculation, sometimes shifting the final digit. Carry extra digits through the working and round only the reported answer. In multi-stage work, keep at least two guard digits beyond your intended precision. This is the opposite of what many students are taught to do by hand.

How do exact numbers and constants affect the count?

They do not limit it. Counted quantities are exact: 12 items is exactly 12, not 12 to two significant figures. Defined conversions are exact too — 1 inch is precisely 2.54 cm by definition. So when multiplying a measurement by an exact factor, the measurement alone determines the significant figures. Treating an exact conversion as a two-figure limit needlessly discards precision.

What is round-half-to-even and why is it used?

When the digit to be dropped is exactly 5 with nothing after it, always rounding up introduces a small systematic upward bias across many values. Round-half-to-even, also called banker's rounding, rounds to the nearest even digit instead: 2.5 becomes 2, 3.5 becomes 4. Over many calculations the biases cancel. Most scientific and financial software uses it by default, which is why a spreadsheet sometimes disagrees with what you expected.