What is a Rational Number

posted on: 12 Jan, 2012 | updated on: 15 Oct, 2012

The Rational Numbers are those numbers which can either be whole numbers or Fractions or Decimals. Rational numbers are the Subsets of Real Numbers and can be written as a Ratio of two integers in the form $\frac{p}{q}$ where 'p' and 'q' are integers and 'q' is non zero.
A Set of rational numbers is denoted by capital Q. The rational numbers are contrasted with Irrational Numbers such like $\pi$, square roots and logarithms of numbers.

These are the some examples of the rational numbers. A rational number is of the form $\frac{p}{q}$ where q is nonzero.

$\frac{1}{1}$ = 1

$\frac{22}{100}$ = 0.22

$\frac{3}{1000}$ = 0.003

What happens if q = 0?

$\frac{90}{0}$ = $\frac{p}{q}$
If the given expression is rational q can't be zero(q≠0). Hence the above expression is not a rational number and it cant be defined.

Note:

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.