Answer:
2 sig figs
Explanation:
The number with the fewest digits defines the significant figures in the final answer. 2.3 has 2 sig figs, less than the 3 sig figs for 5.46. So the answer is limited to 2 sig figs.
2.3 x 5.46 = 12.558 on a calculator
But 13 is the correct answer. 12.558 to 2 sig figs requires rounding; up in this case.
The intent with sig figs is to communicate the precision of the measurements. If these numbers were measures of length, meters, then the 2.3 is stating that the measurement device used was no more accurate than the tenth of a meter. This could prove important if a subsequent experiment depends on more than that level of accuracy. 2.3 tells us that the length is around 2/3 meters, not 2.300 meters (4 sig figs), which would mean that the measurement is accurate to within 1 mm.