The number of decimal places that an answer should be rounded to depends on the amount of significant digits in the operands. According to Tompkins Cortland Community College, the amount to round to should be the smaller of the two significant digit amounts for multiplication and division.
Significant digits in numbers start at the first non-zero digit and end at the last digit. In order to find the amount of significant digits in a number, Hotmath.com advises to count all non-zero digits and any zero digit with a non-zero digit to its left. This avoids a large count for numbers with long strings of zero digits after a significant digit.
If the calculation is multiplication or division, this procedure should be completed for both operands, and the smaller one should be used as the amount to round to. If the calculation is a power or root, the amount to round to should be equal to the significant digit count of the operand, reports Tompkins Community College.