MathIsimple
Significant Figures Calculator

Significant Figures Calculator

Calculate complex mathematical expressions and automatically apply significant figures rules. Perfect for scientific calculations, laboratory work, and educational purposes.

Scientific GradeStep-by-stepLab Ready
Scientific Expression Calculator
Enter mathematical expressions with functions and get results rounded to significant figures

Supports: +, -, *, /, ^, sqrt(), log(), ln(), sin(), cos(), tan(), abs()

Override default selection (1-15)

Significant Figures Rules

Identifying Significant Figures:

  • • All non-zero digits are significant
  • • Zeros between non-zero digits are significant
  • • Leading zeros are NOT significant
  • • Trailing zeros after decimal point are significant
  • • Trailing zeros in whole numbers may/may not be significant

Operation Rules:

  • • Addition/Subtraction: Result limited by decimal places
  • • Multiplication/Division: Result limited by sig figs
  • • Mixed operations: Apply rules step by step
  • • Exact numbers: Don't limit significant figures
Examples & Applications

Common Examples:

0.0234: 3 sig figs (leading zeros don't count)
2.30 × 10³: 3 sig figs (trailing zero is significant)
1200: 2-4 sig figs (ambiguous without notation)

Scientific Applications:

  • • Laboratory measurements and calculations
  • • Engineering design specifications
  • • Quality control in manufacturing
  • • Scientific research data analysis
  • • Chemistry and physics problem solving
Common Mistakes to Avoid

Counting Leading Zeros

Leading zeros (0.00234) are placeholders, not significant figures.

Ignoring Scientific Notation

1.23e4 has 3 sig figs, not 5. The exponent doesn't add digits.

Rounding Too Early

Keep extra digits during calculation, round only the final result.

Example Calculations
Common scientific calculations with significant figures applied
Addition
Expression: 2.3 + 4.567
Result: 6.9
2 significant figures
Multiplication
Expression: 1.23 * 4.5
Result: 5.5
2 significant figures
Square Root
Expression: sqrt(16.0)
Result: 4.00
3 significant figures
Logarithm
Expression: log(100)
Result: 2.0
2 significant figures
Complex
Expression: (2.5 + 3.7) / 2.0
Result: 3.1
2 significant figures
Scientific Notation
Expression: 1.5e3 * 2.0e-2
Result: 3.0e1
2 significant figures
What Are Significant Figures?

Significant figures (sig figs) are the meaningful digits in a number that indicate the precision of a measurement or calculation result.

Rules for Counting Sig Figs:

  • Non-zero digits: Always significant (1.23 = 3 sig figs)
  • Zeros between non-zeros: Significant (102 = 3 sig figs)
  • Leading zeros: Not significant (0.0123 = 3 sig figs)
  • Trailing zeros in decimals: Significant (1.20 = 3 sig figs)
  • Scientific notation: All digits shown are significant

Why They Matter:

  • Indicate measurement precision and uncertainty
  • Prevent false precision in calculations
  • Essential for scientific and engineering work
  • Required for laboratory reports and data analysis
Sig Fig Rules for Operations

Addition & Subtraction:

  • Result limited by least precise decimal place
  • Example: 1.23 + 4.5 = 5.7 (not 5.73)
  • Count decimal places, not significant figures

Multiplication & Division:

  • Result limited by fewest significant figures
  • Example: 2.3 × 4.56 = 10 (not 10.488)
  • Count significant figures in each number

Mixed Operations:

  • Apply rules step by step
  • Use parentheses to control order
  • Keep extra digits during calculation, round at end
Common Mistakes in Sig Fig Calculations

Scientific Notation Errors

  • • 1.23e4 has 3 sig figs, not 5
  • • Don't count the exponent digits
  • • 2.00e-3 has 3 sig figs (trailing zeros count)
  • • Use scientific notation for very large/small numbers

Premature Rounding

  • • Keep extra digits during calculations
  • • Round only the final answer
  • • Intermediate rounding causes errors
  • • Use calculator memory or parentheses

Logarithm Special Cases

  • • log(100) sig figs depend on 100's precision
  • • If 100 has 3 sig figs, result is 2.000
  • • Decimal places in log = sig figs in argument
  • • Anti-logs follow inverse rule

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