Final answer:
The problem involves adding and dividing numbers in scientific notation. The first step is to divide, and then to add the result to the larger number in scientific notation. The result will be very close to the larger number since the smaller number after division does not significantly contribute to the total.
Step-by-step explanation:
The student's question involves the addition and division of numbers expressed in scientific notation. To solve 4.1x10^4 + 3.7x10^-3 / 5.2x10^-3, we will perform each operation step by step, carefully managing exponents to ensure accuracy.
Step 1: Division
Start with the division part of the expression (3.7x10^-3 / 5.2x10^-3). The 10^-3 terms cancel each other out, and you're left with 3.7 / 5.2 which equals approximately 0.7115 (which can be rounded to 0.71 in scientific notation).
Step 2: Addition
Next, we add 4.1x10^4 to the result of the division. Since 0.71 is much smaller than 4.1x10^4, when we add them together, the result will be very close to 4.1x10^4. To combine these numbers accurately, however, we would normally need to express them with the same exponent; in this case, we can see that the smaller number will not significantly affect the larger number’s value.