Question

how many times greater is the value of 3 in 300 than the value of the 3 in 30

Answer 1

Well it sounds like you mean smaller, not greater. 3/300 = 1/100 while 3/30 = 1/10. So 3 out of 300 is 10 times SMALLER than 3 out of 30. 

Answer 2

The value of 3 in 300 is three hundreds. The value of 3 in 30 is 3 tens.
Each time you move one place to the left in place value it is a multiple of ten...so

the 3 in 300 is ten times greater than the value of the 3 in 30.

(30 × 10 = 300)