1. Measurement with an expressed decimal:
Look for the first non-zero digit--it and all digits to its right are significant.
2. Measurement with an understood decimal:
Zeroes that come between the last non-zero digit and the understood decimal place are not significant. To indicate that any of these zeroes should be considered significant you would place a bar over the right-most significant zero.
Examples:
- 0.00341........3 sig. digs.
- 1.0040.........5 sig. digs.
- 0.00005........1 sig. dig.
- 65000..........2 sig. digs.
- 40300..........3 sig. digs.
- 200300.........4 sig. digs.
Operations with Significant Digits
- Any number that represents a numerical count or an exact definition has an unlimited number of sig. digs.
- When superfluous digit(s) is/are less than 5, the preceeding figure is retained without change. When the digit(s) to be dropped is/are greater than 5, the last place retained is increased by 1. When the digit(s) to be dropped is/are 5 exactly (5, 50, 500, etc), the last retained column is rounded off to be even.
- When adding or subtracting numbers, arrange the numbers in columnar form. Retain no column that is to the right of a column containing a doubtful digit.
- In multiplication and division, the result should have no more sig. digs. than the factor having the fewest number of sig. digs.
- The root or power of a number should have as many sig. digs. as the number itself.