Think back to the place value table. What did you notice about the columns? Well, each one is bigger than the one before it. $10$10 units make a ten, $10$10 tens make a hundred, $10$10 hundreds make a thousand and so on, as shown in the picture below.
So when we multiply a number by $10$10, we make it ten times bigger, which means the number moves up a place in the place value table.
A quick way to multiply any whole number by $10$10 is to add a $0$0 at the end.
That moves all our numbers up one place in the place value table, with the $0$0 as a place holder in the units column.
However, this rule is ONLY true for whole numbers, so you have to be careful once fractions or decimals are involved.