Significant figures rules and the trouble with zeros
The rules for counting significant figures, why leading and trailing zeros behave differently, and how ambiguous whole-number zeros are handled.
The core counting rules
Significant figures capture how much of a measured number is actually meaningful. The rules are short: every non-zero digit counts, any zero trapped between non-zero digits counts, and a trailing zero after a decimal point counts because it records real precision. A leading zero never counts; it only positions the decimal point. So 45.09 has four significant figures, 0.0045 has two, and 12.30 has four. This calculator applies exactly these rules by reading the number in exponential form, where the mantissa contains precisely the significant digits and nothing else.
Leading versus trailing zeros
Leading zeros are placeholders. In 0.0045 the two zeros after the decimal point do nothing but shift the 45 into the thousandths place, so they are dropped and the value counts as two significant figures. Trailing zeros are the opposite: writing 12.30 rather than 12.3 is a deliberate claim that the hundredths digit was measured and happened to be zero. That is why keeping trailing zeros matters when you round. When this tool rounds 2 to three significant figures it shows 2.00, not 2, because the two extra zeros are the whole point of the requested precision.
The ambiguous whole-number zero problem
The hardest case is a trailing zero on a whole number, like 1500. Written plainly, there is no way to tell whether the measurement was precise to two figures, three, or four, because a decimal point would be needed to say so. Since this tool reads a plain numeric value, it cannot recover that lost intent, so it treats such trailing zeros as not significant and counts 1500 as two significant figures and 100 as one. If you truly measured three or four figures, the unambiguous way to record it is scientific notation, for example 1.50 times ten to the third for three figures.
Why numeric input loses some precision
Because the value is parsed as a number rather than kept as the exact text you typed, any trailing zero that a number cannot store simply disappears. Type 0.004560 and it is held as 0.00456, so the tool reports three significant figures, not four. This is a limitation of representing the input numerically, and it is called out in the tool itself. When the trailing zero is meaningful to you, round to the number of figures you want and read the preserved string output, or write the value in scientific notation so the precision is never in doubt.