If two integers ‘a’ and ‘b’ are written in a/b form, then this kind of expression is called as a rational expression and this kind of number (a/b) is called as a rational number like 5/7, 3/5. Now we discuss an important property of rational numbers i.e. Rational Numbers are terminating. This means when we find out the value of rational number, then it produces finite and repeating value, which terminates at certain point. We take some examples which define the terminating property of rational number.
Example 1: Find the decimal value of 1/2 and prove that this number are terminating?
Solution: When we calculate the value of 1/2, it produces 0.5 as a result.
Means 1/2 produces finite value 0.5. So, we can say that 1/2 are terminating.
Example 2: Prove that 3/4 are rational number and its value is terminating.
Solution: As we all know that when some number are written in a/b form, then this kind of number are called as a rational number, so we can say that 3/4 is an irrational number.
And when we calculate the decimal value of 3/4, then it produces 0.75 as a result.
Means 3/4 produces finite value 0.75. So, we can say that 3/4 are terminating.
Example 3: Prove that 5/7 are terminating at certain point.
Solution: when we calculate the decimal value of 5/7, then it produces 0.714 as a result.
Means5/7 produces finite value 0.714. So, we can say that5/7 are terminating.
These are some examples, which tell that all rational numbers are terminating at certain point. So, we can say that Rational Numbers are terminating.