Rounding to Significant Figures Calculators

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Significant figures (sig figs) are the meaningful digits in a measured or calculated number that convey the precision of the measurement. Rules for counting sig figs: all non-zero digits are significant; zeros between non-zero digits are significant; trailing zeros after a decimal point are significant; leading zeros are not significant. When rounding to n significant figures, identify the nth significant digit and round based on the next digit (if ≥ 5, round up; if < 5, round down). In calculations: for multiplication/division, the result should have the same number of sig figs as the input with fewest; for addition/subtraction, round to the same decimal place as the least precise input.

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Counting Significant Figures

  • 1234: 4 sig figs (all non-zero digits significant)
  • 1200: ambiguous — 2, 3, or 4 sig figs (use scientific notation to clarify: 1.2 × 10³ = 2 sig figs)
  • 1200.: 4 sig figs (decimal point after trailing zeros → all significant)
  • 0.00456: 3 sig figs (leading zeros not significant)
  • 10.050: 5 sig figs (zero between digits + trailing zero after decimal)

Rounding Rules

To round 47,830 to 3 sig figs: identify 3rd sig fig (8); look at next digit (3 < 5) → round down → 47,800. To round 0.04968 to 2 sig figs: identify 2nd sig fig (9); look at next (6 ≥ 5) → round up → 0.050.

Sig Figs in Calculations

Multiplication/division: result has same sig figs as least precise input. 4.56 × 1.4 = 6.384 → round to 2 sig figs → 6.4. Addition/subtraction: round result to least precise decimal place. 12.11 + 0.6 = 12.71 → round to tenths → 12.7.

Glossary

Significant Figures (Sig Figs)
The meaningful digits in a number reflecting measurement precision; non-zero digits are always significant; leading zeros are not; trailing zeros after a decimal point are; count determines rounding.
Rounding Rules
For n sig figs: if the (n+1)th digit < 5 → round down; ≥ 5 → round up; multiplication/division → result has fewest sig figs of inputs; addition/subtraction → result has fewest decimal places of inputs.
Scientific Notation
A × 10^n; resolves sig fig ambiguity for trailing zeros; 1.20 × 10³ = 3 sig figs; 1.2 × 10³ = 2 sig figs; always write the significant digits explicitly in the coefficient.

Frequently Asked Questions

Significant figures (sig figs or significant digits) indicate the precision of a measurement — how many digits are meaningful and reliable given the precision of the measuring instrument. A measurement of 5.36 cm (3 sig figs) means the value is known to the nearest 0.01 cm; a measurement of 5.4 cm (2 sig figs) is less precise. Why they matter: reporting more digits than your instrument can measure (e.g., 5.360 cm from a ruler only readable to 0.1 cm) implies false precision. Reporting fewer digits loses valid information. Sig figs communicate precision honestly in scientific reporting.

Rules: (1) Non-zero digits: always significant. 345 = 3 sig figs. (2) Zeros between non-zero digits: significant. 1007 = 4 sig figs. (3) Leading zeros: NOT significant. 0.0045 = 2 sig figs (4 and 5 only). (4) Trailing zeros after a decimal point: significant. 4.500 = 4 sig figs. (5) Trailing zeros without decimal point: ambiguous. 1200 could be 2, 3, or 4 sig figs → use scientific notation: 1.2 × 10³ (2 sig figs); 1.20 × 10³ (3 sig figs); 1.200 × 10³ (4 sig figs). (6) Exact numbers (counting): infinite sig figs. 12 eggs, π in a formula — don't limit your calculation.

Steps: (1) Identify the nth significant digit (count from left, starting with the first non-zero digit). (2) Look at the digit immediately following (the n+1 digit). (3) If n+1 digit < 5: round down (keep nth digit unchanged). If n+1 digit ≥ 5: round up (increase nth digit by 1). (4) Replace all digits after nth with zeros (if before decimal) or drop them (if after decimal). Examples: 48,327 to 3 sig figs: nth digit = 3 (the '3'); next digit = 2 < 5 → round down → 48,300. 0.0074961 to 2 sig figs: nth digit = 4 (the '4'); next digit = 9 ≥ 5 → round up → 0.0075.

Multiplication and division: result should have the same number of sig figs as the least precise input. Example: 4.521 × 3.2 = 14.4672 → 3.2 has 2 sig figs → answer = 14 (2 sig figs). Addition and subtraction: result should have the same number of decimal places as the least precise input. Example: 15.4 + 0.032 + 1.01 = 16.442 → least precise = 15.4 (tenths) → answer = 16.4. Mixed calculations: apply addition/subtraction rule at each addition step; apply multiplication/division rule at each multiplication step. In practice: carry extra digits through intermediate steps and round only the final answer to the correct sig figs.