Explain why when you multiply and find one tenth of one tenth, it is equal to one hundredth?

One tenth is one over ten -----> 1/10
It is 10th part of 1.

So, when you do one tenth of one tenth, it is one tenth over 10 ----> (1/10) /10
So, you can consider it as: (1/10) / (10/1). This is only for simplicity.
Now, you have to multiply the denominator of fraction in numerator with the numerator of fraction in denominator i.e., 10 with 10 and this comes in denominator only.

and numerator of fraction in numerator with the denominator of fraction in denominator i.e., 1 with 1.

So, you get, (1*1) / (10*10) = 1/100
This is again the 10th part of one tenth OR 100th part of 1.