Final answer:
The question involves mathematical multiplication and significant figures. When multiplying, the answer should be rounded to the same number of significant figures as the least precise number in the original set of values. This concept is crucial for precision in mathematical calculations but without the complete equation, the blank cannot be accurately filled.
Step-by-step explanation:
The question '125.65 x blank 1,256.5' appears to involve multiplication and the concept of significant figures in mathematics. When calculating with significant figures, one must be careful to express the final result with the correct number of significant digits, which can affect precision and accuracy.
For example, when we multiply two numbers like 38.65 and 105.93, we get a result of 4094.1945. Considering significant figures, if we decide to round the answer to four significant digits (because the number with the least significant figures we started with is 38.65, which has four significant figures), we will get 4,094.
In the same manner, if we multiply the number 125.65 by a certain number to get 1,256.5, and we want to keep three significant figures, we must first calculate the precise answer and then round it to three significant figures. However, without providing the complete calculation or context in this question, we cannot give an exact answer about which number would fill the blank to make the equation correct.
It is also worth noting the example provided to indicate how to express large numbers in scientific notation, which is an important aspect when dealing with significant figures. In the case given, the number 965 is converted to scientific notation as 9.65 × 10², indicating the decimal point has moved two places to the left from its original position.