Question

When 256 is multiplied by a positive power of 10 the 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

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.

Answer 2

In this case, we have the number 256, but in reality, every INTEGER number multiplied by 10 empowered by n, the number of zeros will be equal to n.

This is because, when multiplying by 10, a zero would be put. Now when multiplying to 10 * 10 = 10 ^ 2, it would have 2 zeros in the final product, and so on until leading to 10 ^ n, the result would have n zeros in the final product.