Significant Figures Calculator (Sig Figs)

Significant figures (often shortened to sig figs) are the digits in a number that carry meaning about the precision of a measurement. If you’ve ever looked at a lab report, a survey result, a calculator screen, or a finance spreadsheet and wondered “how many digits should I keep?”, you’re already dealing with significant figures. This page lets you do two practical things instantly: (1) count how many significant figures a value has, and (2) round a value to a chosen number of significant figures.

• Science & labs: report measurements with honest precision (not fake accuracy).
• Engineering: prevent rounding drift and keep specs consistent across calculations.
• Finance & business: avoid misleading “too many decimals” in KPIs, rates, and forecasts.
• School & exams: show the correct level of rounding on homework, tests, and labs.

A number like 12.30 has four significant figures because the trailing zero is meaningful when a decimal point is present. But 1230 is ambiguous: it could mean 3 sig figs (1, 2, 3) or 4 sig figs (1, 2, 3, 0) depending on whether that last zero is a measured digit or just a placeholder. That’s why this calculator includes a toggle for “treat trailing zeros as significant (when no decimal is shown)”.

Rules for counting significant figures

These are the rules this calculator uses (with an optional toggle to handle the “ambiguous trailing zeros” case):

• Non-zero digits are always significant. (Example: 347 has 3 sig figs.)
• Zeros between non-zero digits are significant. (Example: 1002 has 4 sig figs.)
• Leading zeros are not significant. (Example: 0.0045 has 2 sig figs.)
• Trailing zeros are significant if a decimal point is present. (Example: 2.500 has 4 sig figs.)
• Trailing zeros without a decimal point are ambiguous. (Example: 1500 could be 2, 3, or 4 sig figs.) Use scientific notation to remove ambiguity: 1.5×10³ (2 sig figs) vs 1.500×10³ (4 sig figs).
• Scientific notation: the significant figures are the digits in the mantissa (the part before “×10”).

Rounding to N significant figures

Rounding to significant figures is different from rounding to decimal places. Decimal places lock you to the right of the decimal point; significant figures lock you to a total number of meaningful digits, wherever the decimal happens to fall.

To round a number x to n significant figures:

1. Find the order of magnitude (how many digits are before the decimal): k = floor(log10(|x|)).
2. Compute a scale factor so that the first significant digit moves to the ones place: s = 10^(k - n + 1).
3. Round: x_rounded = round(x / s) × s.

This calculator performs equivalent logic safely, and also supports scientific notation input like 3.20e-4.

Worked examples

• Example 1: Count sig figs
  Value: 0.005040
  Leading zeros (0.00) are not significant. The digits 5, 0, 4, 0 are significant because the zero between 5 and 4 counts, and the final zero counts due to the decimal point. Result: 4 significant figures.
• Example 2: Rounding to sig figs
  Value: 98765, round to 3 sig figs → 98800.
  We keep 9-8-7, look at the next digit (6), round up → 9-8-8, then fill remaining places with zeros.
• Example 3: Small numbers
  Value: 0.0007123, round to 2 sig figs → 0.00071.
  We keep “7” and “1”, next digit is “2” so we stay at 0.00071.
• Example 4: Scientific notation removes ambiguity
  1500 (ambiguous) vs 1.500×10^3 (clearly 4 sig figs). If you care about precision in reports, prefer scientific notation.

How this calculator works

Under the hood, the calculator reads your input as text first (so we don’t accidentally lose zeros that matter), then it applies the sig-fig rules above. If you enter scientific notation, it splits the mantissa and exponent and counts the digits in the mantissa (ignoring the decimal point and any leading sign).

When you round to N significant figures, the calculator computes a scale factor and performs rounding in a way that behaves well for large values, tiny values, and negative numbers. You can also choose your preferred output format:

• Auto: picks a clean display (sometimes scientific notation for huge/small values).
• Plain: tries to show a normal decimal form (useful for homework).
• Scientific: always outputs in scientific notation (best for engineering/labs).

Practical tips (accuracy + virality)

• Post-friendly: Enter a number, round it to 2 or 3 sig figs, and screenshot the “steps” panel. Perfect for classroom or study groups.
• Remove drama in group chats: If someone argues about whether 1200 has 2 or 4 sig figs, show them 1.2e3 vs 1.200e3.
• Make your report look professional: Match sig figs across your final results, not your intermediate steps.
• Don’t over-round too early: Keep extra digits during calculations; round only at the end for reporting.

FAQs

• Is 0 a significant figure?

  The number 0 by itself is typically treated as having 1 significant figure because it’s a measured value (not “no digits”). But zeros can be non-significant when they are just placeholders (like leading zeros in 0.0042).

• How many significant figures are in 1000?

  Without a decimal point, 1000 is ambiguous. Many textbooks treat it as 1 sig fig (just “1”) unless context says otherwise. If you mean four sig figs, write 1000. (with a decimal point) or use scientific notation: 1.000×10^3. In this calculator, you can choose whether to treat those trailing zeros as significant.

• What about 1000.0?

  With a decimal point shown, the trailing zeros are significant. So 1000.0 has 5 significant figures.

• How do significant figures differ from decimal places?

  Decimal places count digits to the right of the decimal (like 2 decimal places). Significant figures count meaningful digits from the first non-zero digit onward. That’s why 0.00123 has 3 sig figs even though it has 5 decimal places.

• Why does my rounded answer sometimes show scientific notation?

  Very large or very small values are cleaner in scientific notation (and avoid a long string of zeros). Use the output format selector to force Plain or Scientific display.

• Does this replace proper uncertainty analysis?

  No. Significant figures are a quick reporting convention. In rigorous measurement science you’ll often use uncertainty (±) values, error propagation, and confidence intervals. Sig figs are still a practical “minimum standard” for clear reporting.

Significant figures in calculations (quick rules)

Counting sig figs is step one. The next question is: how many digits should your final answer have after you do math? Different operations follow different conventions:

• Multiplication / Division: your final answer should have the same number of significant figures as the input with the fewest significant figures.
• Addition / Subtraction: your final answer should have the same number of decimal places as the input with the fewest decimal places (not sig figs).

Suppose you multiply 2.4 (2 sig figs) by 3.1416 (5 sig figs). The raw product is 7.53984. Because 2.4 has only 2 significant figures, the result should be reported as 7.5 (2 sig figs).

Add 12.11 and 0.3. The raw sum is 12.41, but 0.3 has only one decimal place, so you report the result as 12.4 (one decimal place).

Common mistakes (and how to avoid them)

• Rounding too early: keep extra digits during intermediate steps, then round once at the end.
• Confusing zeros: leading zeros don’t count, zeros between non-zero digits do count, and trailing zeros depend on the decimal point.
• Mixing “sig figs” and “decimal places” rules: multiplication/division uses sig figs; addition/subtraction uses decimal places.
• Assuming calculators know intent: a calculator can’t tell whether “1200” means 2 or 4 sig figs. Use the toggle or scientific notation.

When to use scientific notation (the pro move)

If you’re publishing results (lab, engineering report, analytics deck), scientific notation is the cleanest way to show both scale and precision. Compare:

• 0.00000045 (hard to read) vs 4.5×10^-7 (clear and compact)
• 120000000 (hard to count zeros) vs 1.20×10⁸ (precision is explicit)

This calculator accepts “e” notation too (e.g., 1.20e8), which is the format many scientific calculators and programming languages use.

Mini study cheat-sheet

• Start counting at the first non-zero digit.
• Zeros between non-zero digits always count.
• Trailing zeros count only if you can see a decimal point (or you explicitly state they are measured).
• To remove ambiguity, use scientific notation: a.bc × 10^n.

Real-world examples you’ve already seen

• Nutrition labels: calories are often rounded to whole numbers because the underlying measurement isn’t precise to decimals.
• Interest rates: APRs may be shown with 2–3 decimals, but internal models often keep more digits to avoid drift.
• Weather: “72°F” is not “72.000°F”. The number of digits signals the intended precision.
• Surveys: a poll result like 52% is usually reported without extra digits because the margin of error is much larger.

Best practice for reporting

If you also have an uncertainty (like ±0.02), report the value to match the uncertainty. For example, if a measurement is 3.14159 ± 0.02, it’s more honest to write 3.14 ± 0.02. Significant figures are a convenient shortcut, but the goal is always the same: communicate precision without pretending you measured more accurately than you did.

Sig figs rules (one-screen summary)

• All non-zero digits count.
• Zeros between non-zero digits count.
• Leading zeros do not count.
• Trailing zeros count only if a decimal is shown (or stated as measured).
• Scientific notation: count digits in the mantissa.

• 0.00450 → 3 sig figs
• 1002 → 4 sig figs
• 1500 (toggle off) → 2 sig figs
• 1.500e3 → 4 sig figs
• 98765 rounded to 3 → 98800

Get the “teacher-approved” answer

• Count sig figs from the first non-zero digit.
• For multiplication/division, match the fewest sig figs.
• For addition/subtraction, match the fewest decimal places.
• If trailing zeros are ambiguous, use scientific notation (e.g., 1.20e3).

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Requested blocks (pasted exactly):

Make this go viral (simple)

• Round a controversial number (like 1200) with the toggle on/off and screenshot the difference.
• Post “Sig figs cheat-sheet” + the steps panel to student groups.
• Use the scientific notation format to settle trailing-zero debates instantly.