Two Different Instructions
Decimal places count digits after the point. Significant figures count meaningful digits from the first non-zero one onward. They are not interchangeable, and a question asking for one will not accept the other.
0.004821 to two decimal places is 0.00, which is useless. To two significant figures it is 0.0048, which preserves the information. That gap is exactly why significant figures exist.
Which Zeros Count
Leading zeros never count: they are placeholders. Zeros between non-zero digits always count, so 4007 has four significant figures. Trailing zeros after a decimal point count, because writing them was a deliberate claim of precision, so 2.50 has three.
Trailing zeros in a whole number such as 1500 are genuinely ambiguous, which is what standard form is for.
Round Once, at the End
Rounding partway through and then continuing compounds the error. Work with full precision throughout and round only the final answer.
A worked example: 2.4 times 3.6 is 8.64, and rounding that to 8.6 at the end is correct. Rounding the inputs first to 2 and 4 gives 8, which is wrong by a margin that grows with every further step.
Choosing a Sensible Precision
An answer cannot be more precise than the data it came from. Measure a room as 3.2 by 4.1 metres and the area is 13.12 square metres on paper, but honestly it is 13 square metres: two significant figures in, two out.
Quoting every digit the calculator offers is not more accurate. It just misrepresents how much you actually know.
The Five Rule and Its Exception
Digits below five round down, five and above round up. Most classrooms stop there, and for schoolwork that is fine.
Statistical work often rounds a bare five to the nearest even digit instead, so 2.5 becomes 2 and 3.5 becomes 4, because always rounding up biases a long series of numbers upward. Use the plain rule unless you are told otherwise.
