Final answer:
To round 0.0006781004 to three significant figures we look at the first three non-zero digits, which are 678. Since the digit following them is less than 5, it does not affect the third significant digit. Thus, the rounded approximation is 0.000678.
Step-by-step explanation:
To match the number with its closest approximation, we are dealing with the concept of rounding in mathematics. The number given is 0.0006781004. When rounding numbers to significant figures, we consider the first non-zero digits. To round this number to three significant figures, we look at the first three non-zero digits, which are 678. The digit to the right of 678 is 1, which is less than 5, so we do not increase the digit 8. Therefore, the approximation of 0.0006781004 to three significant figures is 0.000678.
As an example from the provided information, if we were to round the number 0.0038661 to three significant figures, we would obtain 0.00387 because the fourth significant digit, 6, is greater than 5 and thus the third digit, 6, is rounded up.