when 256 is multiplied by a positive power of 10 number of zeros in the product is related to the power of 10 explain how the number of zeros relates to the power of 10

If you multiply 256 by 10 powered by k, then the number of zeros in the product is k

Step-by-step explanation:

Let x be any integer, if you multiply x by 10 you will have to add one zero at the right of x. If you multiply by 10 again, you will have to add a second zero at the right, thus if you multiply by 100, you will have to add 2 zeros. If you multiply by 1000 = 10*10*10 = 10³ you will have to add 3 zeros and so on.

Therefore, if you multiply 256 by 10^k, then you will have to add k zeros to 256, and as a consequence, the amount of zeros in the product is equal to the power of 10 we are multiplying.

so, converting firstly the mixed fractions to improper fractions and then "adding".