# Significant Digits and When Zero is Significant

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

1. Any number that represents a numerical count or an exact definition has an unlimited number of sig. digs.

2. 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.

3. 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.

4. In multiplication and division, the result should have no more sig. digs. than the factor having the fewest number of sig. digs.

5. The root or power of a number should have as many sig. digs. as the number itself.

 Send questions, comments or suggestions to Gwen Sibert, at the Roanoke Valley Governor's School gsibert@rvgs.k12.va.us Back to Notes Menu