Significant figures

Significant figures record how precisely a value is actually known. The number 4.20 cm claims three significant figures of precision — the trailing zero is deliberate, telling you the measurement was good to the nearest hundredth of a centimetre. Write it as 4.2 cm instead, and you've quietly thrown away that claim of precision, even though the numbers look almost identical.

Zeros are the trickiest part of counting them. Leading zeros, as in 0.0042, never count — they're just placeholders showing where the decimal point is. Trailing zeros after a decimal point, as in 4.20, always count, because there'd be no reason to write them otherwise.

The result of a calculation can never be more precise than its least precise input — multiplying a length known to 2 significant figures by one known to 5 gives an answer that's only trustworthy to 2, no matter how many digits a calculator happily displays.