A calculator lies about how many digits you earned

Multiply 5.348 × 10⁻² by 3.64 × 10⁴, divide by 1.336, and a calculator happily prints 1.45768982 × 10³. Every one of those nine digits looks equally real. Almost none of them are.

A calculated answer can never be more trustworthy than the least trustworthy number that went into it. If one measurement only has three significant figures, no amount of multiplying can make the answer more precise than that.

Multiplying and dividing follow one rule; adding and subtracting follow a different one. Mixing them up is one of the most common marks lost in the whole chapter.