An exact answer has an infinite number of significant figures. For example a square with side exactly 3 has side 3.000... , with an infinite number of zeros, and an area of 9.000..., again with an infinite number of zeros. A square with side 3.0 has area 9.0, both side and area with two significant figures. A square with side 3. has area 9., with one significant figure in each. The number 3 actually represents the exact number 3, with its infinite number of significant figures. Sometimes we get a little sloppy about that and write 3 when we mean 3. or 3.0 or 3.00, and sometimes that's OK. But when significant figures really matter, we need to be careful. The only correct answer to this question would be 9 pi cm^2, because the 3 cm radius is technically exact. Of course if we know this to be a real physical circle, we know that the radius can't be exactly 3 cm. Maybe 3.000 cm, but certainly not 3.000000000 cm because that last 0 would represent a measurement less than the diameter of an atom, and the atoms that make up a physical circle are not only irregularly spaced at the atomic level but are oscillating in place. So if we're talking about an actual physical measurement, as opposed to an ideal geometric figure, there are always limits to the number of significant figures. In such a case 9 pi could still be a good answer, as long as an uncertainty is specified or implied. On a test problem where I'm looking for knowledge of significant figures, you would want to get that right. But in that case the information you were given would be more carefully specified. For example if I said that the area was 78. square meters, or 7.8 * 10^1 square meters, you would want to pay careful attention to the significant figures. The exact answer to the question as stated would be sqrt(78/pi) m. A 2-significant-figure approximation would be 5.0 m.