Standard form of Rational numbers
Numbers which can be expressed in the form of p/q, where p and q are integers is known as rational numbers.
For example: 3/5, 45/1000, -34/44, 1, -9, etc.
But a frequently asked question is to change a given rational number into the standard form. So, what is a rational number in standard form? How is it different from normal rational numbers?
A rational number is made up of a numerator and a denominator. A rational number is said to be in standard form if the Highest Common Factor or the HCF of numerator and denominator is 1.Now, the question arises that how to change any rational number into its standard form?
Procedure to Convert Rational Numbers to Standard Form
- Whenever we have a rational number, first of all, we find the HCF of numerator and denominator, if it is 1 i.e. if the numerator and denominator of the rational number are coprime, then the given rational number is in its standard form.
- If the numerator and denominator are not co-prime, then we start dividing both the numerator and denominator by the common factor of both. We keep on dividing the numerator and denominator with the common factors unless we get a numerator and denominator with HCF 1.
Let us consider the following example, to have a better understanding.
Consider a rational number 16/24. The HCF of 16 and 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 8/12.
Again the HCF is not equal to 1, so we will again divide it by 2. On dividing the numerator and denominator by 2 we get 4/6. Still, we find that the HCF is not equal to 1. So, we will again divide both the numerator and denominator by 2. So, now we finally obtain 2/3. The HCF of 2 and 3 is 1, i.e. 2 and 3 are co-prime. Hence the rational numbers obtained now has an HCF of 1.
Therefore, the standard form of 16/24 = 2/3
This is the way in which we find how to change any rational numbers in standard form.
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