Perform each of the following calculations, and give an answer with the correct number of significant figures:a. 45.7 x 0.034

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for accurately reporting measurements and calculations in chemistry, as it reflects the precision of the data used.

When multiplying measurements, the result should be reported with the same number of significant figures as the measurement with the least significant figures. This rule ensures that the precision of the result is not overstated, maintaining the integrity of the data. For example, in the calculation of 45.7 x 0.034, the number of significant figures in the final answer will be determined by the factor with the fewest significant figures.

Rounding rules dictate how to adjust numbers to reflect the correct number of significant figures. When the digit to be dropped is less than five, the last retained digit remains unchanged; if it is five or greater, the last retained digit is increased by one. Proper rounding is essential in calculations to ensure that the final answer is both accurate and appropriately precise.