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Significant Figures Calculator

Count, round, and calculate with significant figures

Example Numbers

📏Significant Figures Rules

Non-zero digits
Always significant (1, 2, 3...)
Leading zeros
Never significant (0.0123 = 3 sig figs)
Captive zeros
Always significant (105 = 3 sig figs)
Trailing zeros
Significant if after decimal point

🧮Calculation Rules

Addition & Subtraction
Result has same decimal places as the number with fewest decimal places
Multiplication & Division
Result has same number of sig figs as the number with fewest sig figs
Scientific Notation
Clear way to show exact number of sig figs (1.23 × 10³)
Exact Numbers
Have infinite sig figs (counted items, defined conversions)

Significant Figures Calculator Guide

A significant figures calculator rounds numbers to a chosen count of sig figs and shows how many significant figures a number has. It supports scientific notation and explains rounding for calculations.

What is Significant Figures Calculator?

The significant figures calculator identifies sig figs, rounds inputs to a target count, and applies rules for multiplication/division and addition/subtraction, helping students present lab results correctly.

How to Use the Significant Figures Calculator

  1. Enter a number in standard or scientific notation.
  2. Choose target sig figs (e.g., 3 sf, 4 sf).
  3. Calculate to round and see the counted sig figs.
  4. (Optional) apply operation rules to multi-step calculations.
  5. Copy results for lab reports or exam work.

Formulas & Methods

  • Counting rules:
    • All non-zero digits are significant.
    • Zeros between non-zero digits are significant.
    • Leading zeros are not significant.
    • Trailing zeros are significant only if a decimal point is present (e.g., 1200. has 4; 1200 is ambiguous → use scientific notation).
  • Rounding to N sig figs: express as m x 10^k (with 1 <= m < 10), round m to N digits, then convert back.
  • Operations:
    • Multiply/divide: result has min(sig figs) among inputs.
    • Add/subtract: result matches least precise decimal place.

Assumptions & limitations

  • Ambiguous trailing zeros in integers require scientific notation to clarify.
  • Keep extra guard digits in intermediate steps and round once at the end for accuracy.
  • Calculators display rounded values; store more precision internally when possible.

Examples

Example A — Count & round
0.004562 has 4 sig figs (4562). Rounded to 3 sf → 0.00456.

Example B — Scientific notation
12,300 with 3 sf → 1.23 x 10^4. With 5 sf → 1.2300 x 10^4 (zeros now significant).

Example C — Operations
(12.31 x 0.204) -> 2.508... → 3 sf -> 2.51.
4.321 + 0.07 -> 4.391 → round to 2 decimal places → 4.39.

| Input | Sig figs | 3 sf | |---|---:|---:| | 0.003407 | 4 | 0.00341 | | 1200 | ambiguous | 1.20 x 10^3 | | 5.9995 | 5 | 6.00 |

Pro Tips & Best Practices

  • Use scientific notation to make significance unambiguous.
  • For lab work, round once at the end using guard digits.
  • Match units and precision to instrument resolution.
  • State the uncertainty if known; sig figs do not replace error analysis.

Related Calculators

FAQ

Q: What are significant figures?

A: Digits that carry meaning for precision, including all non-zero digits, zeros between non-zero digits, and trailing zeros in decimals.

Q: How do I round to significant figures?

A: Keep the desired number of sig figs starting from the first non-zero digit, then round the next digit using standard rounding rules.

Q: How do operations affect sig figs?

A: For multiplication/division, the result has the least number of sig figs of the factors. For addition/subtraction, match the least precise decimal place.

Q: How does scientific notation help?

A: It clarifies significant figures by making trailing zeros explicit in the mantissa.

Q: Are leading zeros significant?

A: No—leading zeros only locate the decimal point and are not significant.

Call to Action

Enter a number and target sig figs to get clear, correctly rounded values—use operation rules to format full calculations for reports.