Decimal Representation of Rational Numbers

Rational numbers can be represented in decimal forms rather than representing in fractions. They can easily be represented as decimals by just dividing numerator ‘p’ by denominator ‘q’ (as rational numbers is in the form of p/q).

A rational number can be expressed as a terminating or nonterminating, recurring decimal.

For example:

(i) 5/2 = 2.5,

2/8 = 0.25,

7 = 7.0, etc., are rational numbers which are terminating decimals.

(ii) 5/9 = 0.555555555……. = 0.5 ̇,

4/3 = 1.33333….. = 1.3 ̇,

1/6 = 0.166666 ….. = 0.16 ̇

9/11 = 0.818181…… = 0.8 ̇1 ̇ etc., are rational numbers which are nonterminating, recurring decimals.

Representation of rational numbers in decimal fractions makes calculations more easier as compared to that in case of improper rational fractions.

Some of the examples below will show how rational numbers can be represented as decimal fractions:

(i) 2/3 is a rational number which can be written as 0.667 as decimal fraction.

(ii) 4/5 is rational number which can be written as 0.8 as decimal fraction.

(iii) 2/1 is a rational number which can be written as 2.0 as decimal fraction.

So, with the help of the above examples we can see that how easy is to convert rational numbers into decimal fractions.

Also we conclude that these decimal fractions that are converted can be of any type of example (i) shows that decimal fraction is non-terminating. In case of non-terminating decimal fraction we use rules of rounding off decimal fractions so as take final answer more simpler. While examples (ii) and (iii) have terminating decimal fractions, so they are to be written as such only and no use of rounding off decimals is used.

Rational Numbers

Decimal Representation of Rational Numbers

Rational Numbers in Terminating and Non-Terminating Decimals

Recurring Decimals as Rational Numbers

Laws of Algebra for Rational Numbers

Comparison between Two Rational Numbers

Rational Numbers Between Two Unequal Rational Numbers

Representation of Rational Numbers on Number Line

Problems on Rational numbers as Decimal Numbers

Problems Based On Recurring Decimals as Rational Numbers

Problems on Comparison Between Rational Numbers

Problems on Representation of Rational Numbers on Number Line