Question

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

Answer 1

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.