Final answer:
Mike's initial answer of 3 for the first digit of the quotient when dividing 942 by 32 is incorrect. The first digit should be a 2 as 32 goes into 94 two times, not three.
Step-by-step explanation:
The question asks whether Mike's first digit of the quotient when dividing 942 by 32 is correct. He obtained a quotient of 3 with a remainder. To verify if Mike's initial division step is correct, we can apply long division. Mike starts by determining how many times 32 can go into the first three digits, 942.
Performing the division, 32 goes into 94 two times (since 32 x 3 = 96, which is larger than 94), and we write this 2 next to the 9 (of the 942). After subtracting (32 x 2 = 64) from 94, we are left with a remainder of 30. Then, we bring down the 2 from the original 942 to join the 30, making it 302. Now, we determine how many times 32 can go into 302. 32 divides into 302 nine times, since 32 x 9 = 288, and 32 x 10 would be too much, hence the correct digit for the quotient at this place would be 9, not 3.
Therefore, the first digit of the quotient should be 2, not 3. Consequently, Mike's answer of 3 is incorrect for the first digit of the quotient when dividing 942 by 32.