By Laurie Brenner
Updated Aug 30, 2022
In scientific and mathematical contexts, every number that is not zero—whether positive or negative—holds importance. Zero, however, is not merely “nothing”; its value depends on its position within a number. For example, the trailing zeros in 1.00 convey that the value is exactly one dollar, with no cents. These zeros indicate that the measurement is precise to the hundredths place.
Chemists and mathematicians treat leading zeros as placeholders (e.g., 0.25), but they consider zeros that appear between significant digits to be meaningful (e.g., 2.05). Similarly, a zero in 2,501 conveys positional information. The placement of the decimal determines whether a zero is significant.
Three fundamental rules, as outlined by Penn State’s chemistry department, guide the assessment of zeros:
Columbia University’s chemistry faculty elaborate that trailing zeros in a whole number without an explicit decimal are not significant. Thus, the zero in 25.0 is significant, but the zero in 250 is not; it merely serves as a placeholder unless a decimal point is present (e.g., 250.0).
While everyday language might use “zero” to denote emptiness, in mathematics and scientific notation zero can carry precise information. For instance, measuring a quantity as 20.00 versus 20 indicates an exactness to the hundredths place, whereas 20 alone does not reveal the precision regarding tenths or hundredths.
Zeros enable mathematicians, physicists, and researchers to express exact values with an infinite number of significant figures. Writing 1.000000000, for example, signals that each zero after the decimal point is meaningful, reflecting increasing precision. Such exact representations are essential in definitions like 1 meter = 1.00 meters = 1.0000 meters, where each zero indicates a specific positional value.
