Look at several examples of rational number in the form p q ( q ? 0 ) , where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy ?
A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.
Answer: q should not be 0 and can be expressed as a power of 2, or 5, or both.
Let's look at the explanation.
In every terminating rational number, you will find that the denominator is always a power of 2, or 5, or both.
1/4 = 1/22
13/8 = 13/23
23/125 = 23/53
15/20 = 15/22 × 51
All these rational numbers have terminating decimal representations.
Thus, q should not 0 and can be expressed as a power of 2, or 5, or both.