What Are Significant Figures?
Significant figures (sig figs) are the digits in a number that carry meaningful information about its precision. They indicate how precisely a measurement or value is known. Understanding sig figs is essential in science, engineering, and any field that involves measurements.
Rules for Counting Significant Figures
Rule 1: Non-zero Digits
All non-zero digits are always significant.
Rule 2: Captive Zeros
Zeros between non-zero digits are significant.
Rule 3: Leading Zeros
Leading zeros (before non-zero digits) are NOT significant.
Rule 4: Trailing Zeros
Trailing zeros after a decimal point are significant.
Special Cases
Trailing Zeros Without Decimal
Trailing zeros in a whole number without a decimal point are ambiguous. For example, 1200 could have 2, 3, or 4 sig figs. Using scientific notation clarifies this: 1.2 x 10^3 (2 sig figs) vs 1.200 x 10^3 (4 sig figs). Our calculator treats trailing zeros in whole numbers as NOT significant by default.
Scientific Notation
All digits in the coefficient of scientific notation are significant. For example, 3.00 x 10^5 has 3 sig figs.
Rounding to Significant Figures
- Identify the last significant digit you want to keep.
- Look at the digit immediately to the right.
- If it is 5 or greater, round up. If less than 5, round down.
- Replace remaining digits with zeros (or remove trailing digits after a decimal).
Examples
- 0.004560 = 4 significant figures (leading zeros don't count, trailing zero after decimal does)
- 100.00 = 5 significant figures (trailing zeros after decimal count)
- 1200 = 2 significant figures (trailing zeros without decimal are ambiguous, treated as not significant)
- 3.00 x 10^8 = 3 significant figures