Final answer:
The division of 3,050 by 75 results in a quotient of 40 with a remainder of 50. Understanding significant figures is also vital in ensuring accuracy in division. Reciprocals can be a useful tool for making division operations simpler.
Step-by-step explanation:
The question asked by the student involves dividing 3,050 by 75. To find the remainder of this division, we perform the calculation: 3,050 ÷ 75. When we divide these numbers, we get 40 with a remainder of 50. The process of division and understanding remainders is crucial in mathematics, especially when dealing with whole numbers or when precise quotients are required.
Understanding the notion of significant figures is also important in division. In the context of the example provided, dividing 125 by 307 gives 0.4071661238..., but because both starting numbers have three significant figures, the correct rounded answer should also contain three significant figures, hence it would be 0.407.
Another mathematical concept mentioned is the idea of using reciprocals for division. For instance, one eighth of 1,000 is found by multiplying 1,000 by the reciprocal of 8, which is 0.125, resulting in the answer of 125.