Why does a rational number can be written as the ratio of one integer to another?

The word "Rational" is originated from the word "ratio". So, rational numbers are very well related to the ratio concept of ratio. 

Answer: A rational number can be written as the ratio of one integer to another because integers are of terminating decimal.

Explanation:

An integer can be written as a fraction with a denominator 1, thus any integer is a rational number. A terminating decimal can be represented as a fraction using properties of decimals and place values. 

Terminating decimal is a rational number in the form of p/q and q has factors of 2 and 5 only. Hence, all numbers which are terminating decimals and expressed in the form of p/q, where p is an integer and q is a non-zero integer are called Rational numbers. 

Therefore, a rational number can be written as the ratio of one integer to another because integers are of terminating decimal.