Final answer:
The most similar mistake to the student's incorrect multiplication of 305.74 by 100, where they erroneously added zeroes, is found in option B. Both mistakes involve incorrectly adding zeroes instead of properly moving the decimal point.
Step-by-step explanation:
The student incorrectly multiplied 305.74×100 by simply adding zeroes, rather than moving the decimal point. This is a common misunderstanding when working with multiplying decimals by powers of 10. The correct approach is to move the decimal point to the right the same number of places as there are zeros in the multiplier. Hence, 305.74×100 should result in 30574, without any extra decimal places added.
Comparing the student's mistake with other work samples, the most similar mistake would be option B (30.574×100=3057.40). This sample shows the same error of tacking on zeroes without correctly moving the decimal point two places to the right. The correct answer should be 3057.4 (or 3057.40 if one prefers to keep the decimal and zero for clarity), but the mistake in option B is to think that adding zeroes is necessary after moving the decimal point.
When multiplying by powers of 10, it's important to understand both the mechanics of moving the decimal point, as well as the concept behind it, to avoid such errors in calculations.