Question

Find the cubes of $10$, $30$, $100$, $1000$. What can we say about the zeros at the end?

Answer 1

Let us first find the cubes and then identify the pattern

${10}^3=1000,$

${30}^3=900\times 30=27000,$

$100=10000\times 100=1000000,$

$1000=1000000\times 1000=1000000000$

Now, number of zeros in ${10}^3$ is $3$, in ${30}^3$ is $3$, in ${100}^3$ is $6$, in ${1000}^3$ is $9$.

So, the number of zeros at the end is always a multiple of $3$.