A number has the digits 9 and 7. To the nearest 10, the number rounds to 100. what is the number?

The two combinations of two-digit numbers we could have would be 79 and 97.  The only one of those that would round to 100 is 97.  If we added another digit to the number, it would be over 100.  The very smallest three digit number we could have with these two numbers in it would be 179; that would not round to 100.  That means 97 must be our number.