Final answer:
Marc should multiply his dividend, 391, by 10 as well, changing it to 3910, to compensate for rewriting the divisor 9.2 as 92. This maintains the equivalence of the division operation.
Step-by-step explanation:
Marc is dividing 391 by 9.2 and he rewrote the divisor as 92. To maintain the balance of the equation, Marc needs to multiply the dividend by the same power of 10 he used to adjust the divisor. Since moving the decimal one place to the right in the divisor translates to multiplying it by 10, we must apply the same operation to the dividend. Hence, Marc should multiply 391 by 10, converting it into 3910. In essence, revised division would be 3910 divided by 92.
To understand this concept, consider how multiplying or dividing by powers of 10 affects a number. For example, multiplying 1.9436 by 10 shifts the decimal point one place to the right, turning it into 19.436. Similarly, to convert 965 to correct form as 9.65, we track the change as multiplying by 10 to the second power since we moved the decimal two places to the left.
In essence, when adjusting a division problem, altering the divisor by a power of ten requires an equivalent change in the dividend. Marc's alteration of the divisor from 9.2 to 92 (which is multiplying by 10) necessitates that he also multiplies the dividend by 10, changing 391 to 3910.