Before getting into the actual concept of the Decimal Representation of Rational Numbers firstly, let us understand what are rational numbers. Rational Numbers are the numbers that can be expressed in the form of p/q where p q are integers and q is a non-zero number. Whenever we simplify the rational numbers the resultant is the decimals. In this article, we will cover everything on how to expand rational numbers in decimal form all explained with enough examples.

## Decimal Representation of Rational Numbers

Decimal Representation of Rational Numbers is simply converting a rational number to a decimal form having the same mathematical value. We can express a rational number in its decimal form using the long division method. The quotient which we obtain in the long division process is known as the decimal representation of the rational number.  The two types of decimal representation of Rational Numbers are

• Terminating
• Non-Terminating or Repeating

In a long division method if you get the remainder as zero then decimal expansion of such number is called Terminating. And while dividing if the decimal expansion continues and the remainder doesn’t become zero then it is called Non-Terminating.
Decimal Representation of 1/5

Here 1/5 = 0.2 is a terminating decimal since the remainder is 0.

Decimal Representation of 2/3

2/3 =0.66666 the process repeats and the remainder isn’t zero thus 2/3 is a repeating or non-terminating decimal.

### Decimal Representation of Terminating Rational Number

Terminating Decimal Expansion refers to decimal representation or expansion that terminates after a certain number of digits. In the Case of a Terminating Decimal Expansion, you will find the Prime Factorization of the Denominator has no other factors other than 2 and 5.

### Decimal Representation of Terminating Rational Number

In the Case of Non-Terminating but Repeating Decimal Expansion, the decimal representation has an infinite number of digits. However, there is a pattern of numbers that repeats. Rational Numbers whose denominators have factors other than 2 or 5 don’t have a terminating decimal number as result.

### Solved Examples on Decimal Representation of Rational Numbers

Example 1.
Express 1/12 in Decimal Form?

Solution:

Here Divisor = 12, Dividend = 1
Finding the Decimal Form of the given rational number using the long division method we have

Thus 1/12 denoted in decimal form is 0.08333…. Therefore, it is a non-terminating or repeating decimal.

Example 2.
Express 11/24 in decimal form?
Solution:

Here Dividend = 24, Divisor = 11
Finding the Decimal Form of the given rational number using the long division method we have as beow

thus 11/24 denoted in its decimal form is 2.1818….. Thus, it is a non-terminating or repeating decimal.

Example 3.
Express 5/10 in decimal form?
Solution:
Given rational number is 5/10
Divisor = 10, Dividend =5
Performing the Long Division Method we obtain the decimal form as such

5/10 =0.50 It is a Terminating Decimal.