Standard Form of Rational Numbers


 
 
Concept Explanation
 

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 NumberA rational number frac{p}{q} is said to be in the lowest form or simplest form if p and q have no common factor other than 1.

Rational number frac{6}{7} is in the lowest form, but frac{18}{21} 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 frac{p}{q} in the lowest form, we divide its numerator p and denominator q by the HCF of p and q.

A rational number frac{p}{q} 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:

  • The denominator does not have negative sign
  • Rational Numbers are simplified, so that the HCF (Highest Common Factor) of numerator and the denominator is 1
  • Illustration: Convert frac{16}{24} in standard form:

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    Sample Questions
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    Question : 1

    Express the following numbers in standard form :

    1. frac{-247}{-228}

    2. frac{299}{-161}

    Right Option : D
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    Explanation
    Question : 2

    Express 0.358 as a rational number.

    Right Option : D
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    Explanation
    Question : 3

    The standard form of frac{192}{-168} is

    Right Option : B
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    Explanation
     
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