Chemists, mathematicians and scientists who complete equations in their research consider all nonzero numbers to have meaning or significance whether the number is negative or positive. Any number, whether positive or negative, that does not equate to zero essentially represents a nonzero number. However, keep in mind that zero does not mean simply mean "nothing," as sometimes zero numbers have meaning or significance, depending upon their position in the number. For example, a trailing zero behind a decimal does not mean nothing; it conveys information, like the number $1.00 signifies a single dollar, but no change. The trailing zeros after the decimal point represent that change less than a dollar is not present in that representation.
Significant Figure Rules
Chemists and mathematicians consider leading zeros to have no meaning or significance other than that of a placeholder, as in the decimal number 0.25. But they also consider zero in the number 2.05 as meaningful because it conveys information about the tenths position. The same goes for writing 2,501, which also includes information about the zero's position in that number. It boils down to the placement of the decimal.
Whether or not a zero is significant, or meaningful, is governed by a set of rules. Penn State's chemistry department lists the following three rules as basic conditions:
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- "Non-zero digits are always significant."
- "Any zeros between two significant digits are significant."
- "A final zero or trailing zeros in the decimal portion ONLY are significant."
The chemistry department at Columbia University expands on that third rule by clarifying, "Trailing zeros in a whole number with no decimal shown are NOT significant." So a zero in 25.0 is significant, but a zero in 250 is not. Without a decimal present, the zero in the ones position simply acts as a placeholder, but in 250.0, the zero is significant in both the ones position and the tenths position.
The Meaning of Zero
In everyday life, when people say "zero, zip, zilch," they are saying they have nothing. But in mathematics, chemistry and scientific notations and equations, zero as a nonzero number can hold great significance, depending on its position in the number. For example, if you measured something, and the measurement was 20.00 as opposed to 20, this means that – because the zeros appear to the right of the decimal point – the measurement is exact to the hundredths position. The 20.00 number is more exact than the 20 figure, as 20 does not include information about the numbers in the tenths and hundredths position.
Zero numbers allow mathematicians, physicists and essentially any person working with equations or scientific notations to utilize exact numbers that have an infinite number of significant numerals. For example, if you were to write 1.000000000, these are all zeros that have significance, which essentially indicates these numbers have meaning. These numbers indicate information after the decimal and fall under Rule #3. For example, numbers that have definitions, like 1 meter = 1.00 meters = 1.0000 meters = 1.0000000000000000000 meters and so on – each of those zeros refers to tens, hundredths, thousandths and so on, and give meaning to the definition of the number.