Rules for deciding significant figures

Deciding how many digits in a written number are 'significant' — that is, meaningfully measured rather than just placeholders — follows five rules. First, every non-zero digit in a number is significant; for example, 127.34 g has five significant figures (1, 2, 7, 3 and 4). Second, any zero sandwiched between two non-zero digits is significant; for example, 120.007 m has six significant figures. Third, zeros to the left of the first non-zero digit are never significant, because their only job is to fix the position of the decimal point rather than to record a measured value; for example, 0.025 has just two significant figures (2 and 5), and 0.005 has just one (5). Fourth, zeros at the very end of a number ARE significant if they sit to the right of the decimal point, because a decimal point in a measurement signals a genuinely finer least count of the instrument that produced it; but terminal zeros in a number with no decimal point shown are NOT taken as significant. For example, 0.400 g has three significant figures, since it implies the value was read on a balance with a least count of 0.001 g; but plain 400 g has only one significant figure, while $4.0 \times 10^2$ g (two significant figures) and $4.00 \times 10^2$ g (three significant figures) show how scientific notation is used to state the intended precision unambiguously, corresponding to instrument least counts of 1 g, 0.1 g and 0.01 g respectively. Fifth, in a number already written in scientific notation, every digit of the coefficient counts as significant; for example, $2.035 \times 10^2$ has four significant figures, a …