Significant figures are the digits in a number that carry meaningful information about its precision or accuracy. The key rules for counting significant figures are:
- All nonzero digits are significant. For example, "846" has 3 significant figures.
- Zeros between nonzero digits are significant. For example, "1002" has 4 significant figures.
- Leading zeros (zeros before the first nonzero digit) are not significant. For example, "0.0012" has 2 significant figures.
- Trailing zeros are significant only if there is a decimal point present. For example, "3.50" has 3 significant figures, but "3500" without a decimal point has only 2 significant figures.
- In scientific notation, the significant figures are counted only in the coefficient part. For example, 4.50×1034.50\times 10^34.50×103 has 3 significant figures.
In measurements, significant figures include all certain digits plus the first uncertain digit, reflecting the precision of the measuring instrument. Thus, the number of significant figures in a number depends on these rules and the way the number is written, indicating the precision of the measurement or value.
