Final answer:
The number of partial products in a multiplication calculation can vary depending on the algorithm used. In this case, the difference in the number of partial products is due to a difference in the multiplication algorithms used for the two calculations.
Step-by-step explanation:
The reason there are three partial products in the calculation 273 x 346, but only two partial products in the calculation 273 x 306, is because of a difference in the multiplication algorithms used. In the first calculation, the numbers have three and four significant figures respectively, so the final answer is limited to three significant figures. In the second calculation, the numbers have four and three significant figures respectively, so the final answer is also limited to three significant figures.