Final answer:
In multi-step calculations, operations must follow the PEMDAS order. Significant figures should be carried through without intermediate rounding until the final step. This maintains accuracy and reduces compounded error when dealing with multiplication and division especially.
Step-by-step explanation:
When calculations involving more than one arithmetic operation are required, certain rules must be followed to ensure the correct sequence of operations. These rules are known by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This means that you perform any operations inside parentheses first, then calculate exponents, followed by multiplication and division in order from left to right, and finally addition and subtraction from left to right.
For chemists or students performing calculations on paper, it is crucial to handle significant figures accurately. One should carry all possible digits from intermediate calculations into the next step to avoid compounding inaccuracies through rounding. After the final calculation step, the final answer should then be rounded to the correct number of significant figures. For example, when performing a chain of multiplications or divisions, it's important to limit the significant figures to that of the datum with the least number to ensure the final reported answer is as precise as possible.
In terms of actual operations, if we are dealing with multiplication or division, multiply or divide as required, carrying as many digits as possible without rounding until the end. This minimizes the compounded error that can occur with intermediate rounding and ensures a more accurate final answer. Always keep track of significant figures and units throughout the calculations.