# Mathematics Summary Unit-1 Number System: Standard form of a Rational Number and Equivalent Forms of a Rational Number

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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