Final answer:
The Mathswatch question related to mathematical operations requires understanding the concepts behind addition, subtraction, multiplication, and division, particularly the importance of significant figures in these calculations.
Step-by-step explanation:
Understanding Mathematical Operations
To address the Mathswatch question regarding mathematical operations, it is essential to grasp the concepts behind addition, subtraction, multiplication, and division. One basic principle in working with addition and subtraction is to pay attention to the order of operations, as well as the positive or negative signs of the numbers involved. When dealing with whole numbers, it is crucial to align the digits properly according to their place value.
In terms of multiplication and division, you should count the number of significant figures in each number and round the result to match the number with the fewest significant figures. This ensures precision and accuracy in mathematical calculations. For multiplication, remember that two positive numbers or two negative numbers will result in a positive product, while multiplying numbers with opposite signs will result in a negative product. Similarly for division, the rules for determining the sign of the quotient follow the multiplication rules.
For example, multiplying 0.6238 cm by 6.6 cm requires rounding the result to the number of significant figures present in the number with the least, which in this case is 6.6 cm with two significant figures. When dividing 421.23 g by 486 mL, we must round our result to match the least number of significant figures present in either value involved in division.