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Significant Figures Calculator

Count · Round · Scientific Notation · Operations

Count sig figs in any number, round to N significant figures, convert to scientific notation, and apply the correct sig fig rules to arithmetic operations.

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Round to N Sig Figs

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Enter Up to 5 Numbers

Batch Analysis Results

Number	Sig Figs	Digit Breakdown	Scientific Notation

Sig Fig Rules Reference

All non-zero digits are significant

1, 2, 3, 4, 5, 6, 7, 8, 9 are always significant wherever they appear.

Example: 1234 → 4 sig figs

Leading zeros are NOT significant

Zeros before the first non-zero digit are only placeholders.

Example: 0.0045 → 2 sig figs (4 and 5)

Zeros between non-zero digits are significant (captive zeros)

Any zero sandwiched between two non-zero digits is significant.

Example: 1007 → 4 sig figs

Trailing zeros after a decimal point ARE significant

If a number has a decimal point, all trailing zeros are significant — they indicate precision.

Example: 3.140 → 4 sig figs; 0.000100 → 3 sig figs

Trailing zeros in integers (no decimal) are ambiguous

1200 could be 2, 3, or 4 sig figs. Scientific notation resolves this: 1.2 × 10³ = 2 sig figs; 1.200 × 10³ = 4 sig figs.

Example: 1234500 → 4–7 sig figs (ambiguous)

Exact numbers have infinite significant figures

Counted values (12 eggs) and defined constants (1 inch = 2.54 cm exactly) have infinite sig figs and do not limit precision in calculations.

Example: 12 eggs × 2.5 g = 30 g (2 sig figs, limited by 2.5)

What Are Significant Figures?

Significant figures (also called significant digits or sig figs) are the digits in a number that carry meaningful information about its precision. In science, engineering, and mathematics, every measurement has a limited precision determined by the instrument used. Significant figures communicate that precision — they tell you how many digits of a reported value can be trusted.

For example, if a chemistry balance reads 12.34 g, you know the mass to the nearest 0.01 g, and the number has 4 significant figures. If instead you write 12.340 g, the trailing zero signals that the balance was precise to 0.001 g — and that number has 5 significant figures.

The Six Sig Fig Rules

There are six core rules that determine whether a digit is significant:

Rule	Example	Sig Figs
All non-zero digits are significant	6.022	4
Leading zeros are NOT significant	0.0045	2
Captive zeros (between non-zeros) are significant	1007	4
Trailing zeros after a decimal ARE significant	3.140	4
Trailing zeros in integers are ambiguous	1200	2, 3, or 4
Exact/defined numbers have infinite sig figs	12 eggs	∞

Precision vs. Accuracy

Precision refers to how repeatable or consistent a measurement is — how many significant figures it contains. Accuracy refers to how close a measurement is to the true value. A thermometer that consistently reads 100.3 °C when the water is at 100.0 °C is precise (3 sig figs, consistent) but inaccurate (off by 0.3 °C). Significant figures capture precision, not accuracy.

Sig Figs in Arithmetic Operations

Addition and Subtraction

Round the result to the same number of decimal places as the measurement with the fewest decimal places. For example:

Numbers	Exact Sum	Rounded Answer	Reason
12.11 + 18.0 + 1.013	31.123	31.1	18.0 has 1 decimal place
100. + 23.643	123.643	124	100. has 0 decimal places

Multiplication and Division

Round the result to the same number of significant figures as the measurement with the fewest sig figs. For example:

Numbers	Exact Result	Rounded Answer	Reason
4.56 × 1.4	6.384	6.4	1.4 has 2 sig figs
22.37 ÷ 3.10	7.2161...	7.22	3.10 has 3 sig figs

Scientific Notation and Sig Figs

Scientific notation expresses a number as a coefficient between 1 and 10 multiplied by a power of 10 — for example, 6.022 × 10²³ (Avogadro's number). Every digit in the coefficient is significant, which eliminates the ambiguity of trailing zeros in integers. Writing 1.200 × 10³ unambiguously signals 4 significant figures, while 1200 is ambiguous.

Engineering notation is a variant where the exponent is always a multiple of 3, matching SI prefixes (kilo, milli, micro). For instance, 0.00420 becomes 4.20 × 10⁻³ in scientific notation and 4.20 × 10⁻³ in engineering notation (the same here, since −3 is already a multiple of 3).

Worked Examples from Chemistry

Molar Mass Calculation

The molar mass of water (H₂O) is calculated from atomic masses: H = 1.008 g/mol, O = 15.999 g/mol. The calculation gives 2 × 1.008 + 15.999 = 18.015 g/mol. Since all values are known to 3–5 decimal places, the result is valid to 3 decimal places, yielding 18.015 g/mol (5 sig figs).

Concentration Calculation

If you dissolve 3.45 g of NaCl (molar mass 58.44 g/mol) in 250.0 mL of water, the moles = 3.45 / 58.44 = 0.05902... mol. The concentration = 0.05902 / 0.2500 L = 0.2361 mol/L. Since 3.45 has 3 sig figs (the limiting value), the answer rounds to 0.236 mol/L.

Why Sig Figs Matter in Science

Significant figures prevent the reporting of false precision — a critical concern in physics, chemistry, biology, and engineering. A distance measured with a ruler marked in centimeters should not be reported to six decimal places even if a calculator produces those digits. Proper application of sig fig rules ensures scientific communication is honest about the limits of measurement instruments and experimental procedures.

Frequently Asked Questions

What are significant figures?

Significant figures are the meaningful digits in a number that indicate its precision. They include all non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point. Leading zeros are never significant. For example, 0.00420 has 3 significant figures: 4, 2, and the trailing zero after the 2.

Are leading zeros significant?

No. Leading zeros — zeros that appear before the first non-zero digit — are never significant. They only serve as placeholders to indicate magnitude. For example, in 0.0045, the three zeros before the 4 are all non-significant. This number has just 2 significant figures.

Are trailing zeros significant?

It depends on context. Trailing zeros after a decimal point are always significant — for example, 3.140 has 4 sig figs. Trailing zeros in whole integers without a decimal point are ambiguous; 1200 could have 2, 3, or 4 sig figs. Scientific notation eliminates this ambiguity: 1.200 × 10³ clearly has 4 sig figs.

How do you round to significant figures?

To round a number to N significant figures: (1) identify the Nth significant digit, (2) look at the digit immediately after it, (3) if that digit is 5 or greater, round the Nth digit up; if less than 5, leave it unchanged, (4) replace all subsequent digits with zeros (for integers) or drop them (after a decimal). For example, rounding 3.14159 to 3 sig figs gives 3.14.

How do sig figs work in addition and subtraction?

For addition and subtraction, round the result to the same number of decimal places as the measurement with the fewest decimal places — not the fewest significant figures. For example, 12.11 + 18.0 + 1.013 = 31.123, but since 18.0 has only 1 decimal place, the answer rounds to 31.1.

How do sig figs work in multiplication and division?

For multiplication and division, round the result to the same number of significant figures as the measurement with the fewest significant figures. For example, 4.56 × 1.4 = 6.384, but since 1.4 has only 2 sig figs, the answer rounds to 6.4.

What is scientific notation and how does it relate to significant figures?

Scientific notation expresses a number as a coefficient (between 1 and 10) multiplied by a power of 10, such as 6.02 × 10²³. It removes all ambiguity about significant figures because every digit written in the coefficient is significant. For example, 1.20 × 10³ unambiguously has 3 significant figures, while the equivalent 1200 is ambiguous.