Scales, Standards, Units and Significant Figures

Each non-zero digit within a number is classified as a significant figure.
Zeros are included in the count of significant figures only under specific conditions:
- When they are positioned between two non-zero digits.
- When they are located at the end of the decimal part of a number.
Examples identified in practice include:
- The number $2000$ contains only $1$ significant figure, which is the digit $2$ .
- The number $2000.0$ contains $5$ significant figures, as the trailing zero in the decimal part is counted.

To estimate a number to a specific precision, significant figures are removed starting from the right until the desired number of significant figures is reached.
Rounding must be applied as figures are removed to ensure accuracy.
Example of rounding procedure:
- The value $6.827$ possesses $4$ significant figures.
- If this value must be expressed to $3$ significant figures, the digit $7$ must be removed.
- Because the digit $7$ is removed, the preceding digit is rounded up, resulting in a value of $6.83$ .

When handling experimentally measured values of varying significant digits, specific rules must be applied during addition and subtraction.
Rule for Addition and Subtraction:
- When two experimentally measured numbers are added or subtracted, the total number of significant figures or digits in the final result must be equal to the smallest number of decimal places found in any individual term within the sum or difference.
Example Application of the Addition Rule:
- Consider the addition of two measured values: $9.65$ and $8.4$ .
- The term providing the limiting precision is $8.4$ , as it contains the least number of decimal places (one decimal place) compared to $9.65$ .
- While the mathematical sum of these values is $18.05$ , the reported experimental sum must be rounded to match the least precise term.
- Consequently, the correct sum is $18.1$ and not $18.05$ .