Significant Zeros Rules

Overview

This lecture covers the rules for determining when zeros are significant in significant figures, including specific examples for clarity.

Zeros between nonzero digits are always significant.
Example: In 3,901, all four digits are significant.
Multiple zeros between nonzero digits are all significant (e.g., 1,009,003 has seven significant figures).
Decimal points do not affect the significance of sandwiched zeros.

Zeros to the left of all nonzero digits are never significant.
Example: In 0.000491, only 4, 9, and 1 are significant (three significant figures).
The quantity of leading zeros does not matter; none are significant.

Zeros to the right of nonzero digits are significant only if there is a decimal point present.
Example: In 83,000 (no decimal), only 8 and 3 are significant (two significant figures).
In 83,000. (with a decimal), all five digits are significant.
In 83.000, all five digits are significant because of the decimal point.
In 4,500 (no decimal), zeros are not significant; total significant figures depend on nonzero digits.
In 200. (decimal present), all three digits (including zeros) are significant.

If zeros are to the right of nonzero digits, they are significant only when a decimal point is present.

Significant Figures — Meaningful digits in a number, used to show the precision of measurements.
Sandwiched Zeros — Zeros between nonzero digits; always significant.
Leading Zeros — Zeros before the first nonzero digit; never significant.
Trailing Zeros — Zeros to the right of nonzero digits; significant only with a decimal point.