Significant Figures Calculator

Count sig figs, round to significant figures, and perform calculations with proper precision

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Significant Figures Rules

  • • Non-zero digits are always significant
  • • Zeros between non-zeros (trapped) are significant
  • • Leading zeros are never significant
  • • Trailing zeros after decimal ARE significant

Supports scientific notation (e.g., 3.5e8 or 3.5×10⁸)

Quick Examples

Significant Figures Count Rounded Result

significant figures

Digit-by-Digit Analysis

Digit Significant? Reason

Original Number

sig figs

Rounded Number

sig figs

Quick Reference Table

Example Sig Figs Rule Applied
1234 4 All non-zero digits
1007 4 Trapped zeros count
0.0045 2 Leading zeros don't count
12.00 4 Trailing zeros after decimal
1200 2 Trailing zeros ambiguous

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About Significant Figures Calculator

What Are Significant Figures?

Significant figures (sig figs) are the digits in a number that carry meaningful contributions to its precision. They indicate the reliability of a measurement and help avoid overstating the accuracy of calculated results.

Rules for Counting Significant Figures

1. Non-Zero Digits

All non-zero digits are always significant.

  • 1234 has 4 significant figures
  • 56.78 has 4 significant figures

2. Zeros Between Non-Zero Digits (Trapped Zeros)

Zeros sandwiched between non-zero digits are significant.

  • 1007 has 4 significant figures
  • 5.0023 has 5 significant figures

3. Leading Zeros

Leading zeros (before the first non-zero digit) are never significant - they are placeholders.

  • 0.0045 has 2 significant figures
  • 0.000123 has 3 significant figures

4. Trailing Zeros

  • With a decimal point: Trailing zeros are significant
    • 12.00 has 4 significant figures
    • 100. has 3 significant figures
  • Without a decimal point: Trailing zeros may or may not be significant (ambiguous)
    • 1200 has 2-4 significant figures (ambiguous)

5. Exact Numbers

Exact numbers (counted values, defined constants) have infinite significant figures.

  • 12 eggs (counted)
  • 60 seconds/minute (defined)

Significant Figures in Calculations

Multiplication and Division

The result should have the same number of sig figs as the measurement with the fewest significant figures.

Example: 4.56 × 1.4 = 6.384 → 6.4 (2 sig figs)

Addition and Subtraction

The result should have the same number of decimal places as the measurement with the fewest decimal places.

Example: 12.11 + 3.3 = 15.41 → 15.4 (1 decimal place)

Rounding Rules

  1. If the digit to drop is < 5, keep the last retained digit the same
  2. If the digit to drop is > 5, increase the last retained digit by 1
  3. If the digit to drop is exactly 5:
    • Round to the nearest even number (banker's rounding)
    • Or always round up (standard rounding)

Common Examples

Number Sig Figs Explanation
1234 4 All non-zero digits
0.00234 3 Leading zeros don't count
1020 3 Trapped zero counts
100.0 4 Trailing zero with decimal
3.00 × 10⁸ 3 Scientific notation is clear

Tips for Using This Calculator

  1. Count Mode: Enter any number to count its significant figures
  2. Round Mode: Specify the desired number of sig figs for rounding
  3. Calculate Mode: Perform operations with automatic sig fig handling

Why Significant Figures Matter

Significant figures ensure that calculated results don't imply more precision than the original measurements support. This is essential in:

  • Scientific research
  • Laboratory work
  • Engineering calculations
  • Medical dosing
  • Quality control

Note: This calculator follows standard significant figure rules taught in chemistry and physics courses.