Define Significant Figures and write rules for counting significant figures.
SIGNIFICANT FIGURES
In any physical measurement, significant figures are defined as all the accurately known digits plus the first doubtful (estimated) digit. Every physical measurement involves some degree of uncertainty caused by human limitations, instrumental limitations, or both. Therefore, the number of significant figures directly reflects the precision and reliability of a measured value. The last digit, while reasonably correct, contains an estimate that guarantees the certainty of the preceding digits.
RULES FOR COUNTING SIGNIFICANT FIGURES
- (i) Whole Numbers: In whole numbers, all non-zero digits are recognized as significant. Zeros written at the right side (trailing zeros) are generally not counted as significant figures unless indicated by a decimal point or measurement precision.
- (ii) Decimals and Leading Zeros: In a decimal number, trailing zeros at the right side of a non-zero digit are counted as significant figures. However, leading zeros at the left side are placeholders and are not taken as significant figures.
- (iii) Powers or Exponents: When quantities are expressed in scientific notation, powers or exponents to a certain base ($10^n$) are completely omitted and are not taken as significant figures.
- (iv) Addition and Subtraction Process: When adding or subtracting measurements, the final result must be rounded off to contain only as many decimal places as are contained in the component value with the least number of decimal places.
- (v) Multiplication and Division Process: When multiplying or dividing measurements, the final result must be rounded off to contain only as many significant figures as are contained in the factor with the least number of significant figures.
EXAMPLES
| S.No | Value | No. of Significant Figures | Identified Digits |
|---|---|---|---|
| 1 | 0.00045 | 2 | 4, 5 |
| 2 | 1.2000 | 5 | 1, 2, 0, 0, 0 |
| 3 | 505 | 3 | 5, 0, 5 |
| 4 | 34000 | 2 | 3, 4 |
| 5 | $6.67 \times 10^{32}$ | 3 | 6, 6, 7 |
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