Standard Form of Rational Numbers

A rational number is said to be in Standard Form if the numerator and the denominator are co-prime numbers. It is also called the simplest form of Rational Number.  A rational number is said to be in the lowest form or simplest form if p and q have no common factor other than 1.

Rational number is in the lowest form, but is not in the lowest form as 18 and 21 are not co-prime because both of them have a common factor 3. In order to reduce a rational number in the lowest form, we divide its numerator p and denominator q by the HCF of p and q.

A rational number is said to be in standard form, if it s denominator q is a positive integer and p and q have no common divisor other than 1.

In the Standard form:

Illustration: Convert in standard form:

Solution: The HCF of numerator 16 and denominator 24 is 8, which is not equal to 1. Hence the given rational number is not in its standard form. Now, we know that 2 is the common factor of 16 and 24.  Dividing both the numerator and denominator by 2, we get

  .

Again the HCF of numerator 8 and denominator 12 is not equal to 1, so we will again divide it by 2 as it is the common factor of 8 and 12. Repeat the same process, until the HCF = 1.

Repeat the same process, as the HCF of numerator 4 and denominator 6 is not equal to 1, so we will again divide it by 2 as it is the common factor of 4 and 6.The process is repeated till we get the HCF as 1

Now the HCF of numerator 2 and denominator 3 is equal to 1. Hence it is the lowest form or standard form

Therefore, the standard form of

Illustration: Express 0.65 as rational number.

Solution:To express 0.65 in the standard from we will first convert it into fraction and then to the simplest form.