Why 1.0 and 1 are not quite the same number to a scientist
Write 1 and you are claiming one digit of certainty; write 1.0 and you are claiming two. Significant figures are the digits in a measurement that genuinely carry information, and they quietly tell a reader how carefully something was measured. Pad a result with extra decimals and you have invented precision you never had.
Take a ruler marked in millimetres that gives a reading of 114.8 mm. The 1, 1 and 4 are certain. The final 8 is an estimate between marks, uncertain but still meaningful, so it counts too, giving four significant figures. Likewise a volume of 2.98 litres, known to within 0.05 litres, has three significant figures, because each digit narrows down where the true value lies even if the last one is a little fuzzy.
Zeros cause most of the confusion. Leading zeros never count: 0.052 kilometres is just 52 metres, and the zeros vanish when the unit changes, so they carry no information about precision. Zeros trapped between other digits always count. Trailing zeros after a decimal point count if the instrument could resolve them, so 1.200 has four. But a distance written as 1500 metres, measured only to the nearest hundred, has just two; the zeros are placeholders.
The digit on the far left, holding the largest place value, is called the most significant, and the rightmost meaningful digit is the least significant. Anything beyond that is spurious, often produced when a calculation spits out more decimals than the original data justified. Reporting 12345.25 grams from a scale accurate only to the nearest gram creates false precision; the honest figure is 12345 grams, and the discarded 0.25 grams roughly reflects the scale's resolution.
Rounding is the fix. A set of approximate rules, called significance arithmetic, helps carry the right number of digits through calculations, while scientists use the more rigorous propagation of uncertainty. Not all rounding is about precision, though: news reports often round numbers simply to make them easier to hear.
Source: Significant figures
