# Mathematics Summary Unit-1 Number System: Standard Form of a Rational Number and Equivalent Forms of a Rational Number (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Standard Form of a Rational Number

We know that numbers of the form

• In each of the above case, we have made the denominator q as positive.
• A rational number , where p and q are integers and , in which q is positive (or made positive) and p and q are co-prime (i.e.. when they do not have a common factor other than 1 and – 1) is said to be in standard form.
• Thus, the standard form of the rational number . Similarly, are rational numbers in standard form.

Example: Which of the following are rational numbers and which are not?

Solution:

(i) can be written as , which is of the form . Therefore, is a rational number.

(ii) is a rational number, as it is of the form of .

(iii) is also a rational number as it is of the form .

(iv) Similarly, are all rational numbers according to the same argument.

## Equivalent Forms of a Rational Number

A rational number can be written in an equivalent form by multiplying/dividing the numerator and denominator of the given rational number by the same number.

For example,

etc. are equivalent forms of the rational number .

Example: Write five equivalent forms of the following rational numbers:

(i) (ii)

Solution:

(i)

Therefore, five equivalent forms of are

(ii) As in part (i) , five equivalent forms of are

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