Significant figures (or significant digits) refer to the digits in a number or measurement that carry meaning and contribute to its precision and accuracy. They indicate the level of certainty in a measurement, including all the digits that are known with confidence plus one estimated digit. For example, in the number 13.2, there are 3 significant figures because the digits 1 and 3 are certain, and 2 is estimated. Significant figures are important in scientific and technical measurements because they reflect the reliability of the measured or calculated value. The rules for determining significant figures include:
- All non-zero digits are significant (e.g., 652.1 has 4 significant figures).
- Zeros between non-zero digits are significant (e.g., 4005 has 4 significant figures).
- Leading zeros before the first non-zero digit are not significant (e.g., 0.0034 has 2 significant figures).
- Trailing zeros after a decimal point are significant (e.g., 7.00 has 3 significant figures).
- Trailing zeros in a number without a decimal point may or may not be significant depending on context (e.g., 2650 can have 3 or 4 significant figures depending on how it is written).
In summary, significant figures express the precision of a measured quantity or calculation by including all meaningful digits that contribute to its accuracy.
