Significant figures (or significant digits) are the digits in a number that carry meaningful information about its precision and reliability. They include all the certain digits plus one estimated digit in a measurement or calculation, reflecting the accuracy of the value.
Key Points About Significant Figures:
- They begin with the first non-zero digit from the left and end with the last digit that is either non-zero or a zero considered exact or measured.
- Significant figures indicate the precision of a measurement or calculated value, showing which digits are reliable and which are estimated.
- The number of significant figures depends on the measurement instrument's precision and the method of calculation.
Rules for Identifying Significant Figures:
- All non-zero digits are significant. For example, 211.8 has four significant figures.
- Zeros between non-zero digits are significant. For example, 20,007 has five significant figures.
- Leading zeros (zeros before the first non-zero digit) are not significant; they only indicate the decimal place. For example, 0.0085 has two significant figures.
- Trailing zeros in a number with a decimal point are significant. For example, 12.000 has five significant figures.
- Trailing zeros in a whole number without a decimal point are not significant unless specified. For example, 320 has two significant figures, but 320. (with a decimal) has three.
- Exact numbers (like defined conversion factors or constants such as π) have an infinite number of significant figures.
Examples:
- Measurement 114.8 mm with a ruler marked in 1 mm increments has four significant figures: the first three digits (114) are certain, and the last digit (8) is estimated.
- A volume of 2.98 L with an uncertainty of ±0.05 L has three significant figures because all digits contribute to the precision within the uncertainty range.
Significant figures are crucial in scientific reporting because they communicate the precision of measurements and ensure that calculations do not imply greater accuracy than the data supports
