In this chapter, we will learn to convert rational number into decimal numbers with examples.

At the end of the chapter, some problems are also given for your practice.

## How to convert rational number into decimals ?

We know that **rational numbers are represented in the form of fraction** \mathtt{\ \frac{p}{q}} .

Where both** p and q are integers**.

To convert the rational number into decimals,** simply divide the numerator and denominator** and write the quotient as a result.

Note that after division, **you will get two type of decimals;**

(a) **Terminating decimals**

This decimal value will terminate after some digits.

(b)** Non terminating decimals**

The decimals with infinite number of digits. In this case, we will take approximate value of the quotient.

### But why we are converting rational number into decimal in first place ?

Because doing mathematical operations like addition/subtraction is much easier than the rational numbers.

In higher mathematics, you will be asked to solve complex math problems. **Doing math calculations using decimal number will be much easier and time saving**.

### Examples of Rational number to decimal number conversion

Given below are examples of writing rational numbers in decimal form.**Example 01**

Convert 2/5 into decimal.**Solution**

Divide numerator by denominator.

\mathtt{\frac{2}{5} \Longrightarrow \ 0.4}

Hence, the rational number is converted into terminating decimal.

**Example 02**

Convert 12 / 3 into decimal number.**Solution**

\mathtt{\frac{12}{3} \Longrightarrow \ 4.0}

Here we again get terminating decimal.

**Example 03**

Convert 100/3 into decimal form.**Solution**

\mathtt{\frac{100}{3} \Longrightarrow \ 33.3333…….}

Here we get non terminating decimal.

Here we will take the approximate value of 33.33 as a solution.

**Example 04**

Convert 50/7 in decimal form.**Solution**

Dividing numerator by denominator.

\mathtt{\ \frac{50}{7} \Longrightarrow \ 7.14285714286}

Note that the given solution has too many decimal places. It will be convenient to take the approximate value of the number.

⟹ 7.14285714286

⟹ 7.14 (approx.)

Hence, **7.14 is the solution.**

**Example 05**

Convert 12/5 into rational number.

**Solution**

Dividing numerator by denominator.

\mathtt{\ \frac{12}{5} \Longrightarrow \ 2.4}

Hence, 2.4 is the solution.

I hope you understood the above examples. Given below are some problems for practice.

## Rational number to decimals – Solved Problems

(01) Convert the given rational numbers into decimals. Check if the resulting decimal is terminating or non – terminating.

(a) 11/5

(b) 100/6

(c) 13 / 7

(d) 8 / 9

(e) 50 / 2

(f) 75 / 10

(g) 69 / 11

(h) 14 / 4

(i) 18 / 9

(j) 105 / 7

**Solution**

To convert the given rational number in decimal form, simply divide numerator by denominator.

**(a) 11/5**

\mathtt{\frac{11}{5} \Longrightarrow \ 2.2}

Here **2.2 is a terminating decimal**.

**(b) 100/6**

\mathtt{\frac{100}{6} \Longrightarrow \ 16.6666.\ .\ .\ .}

Here 16.6666. . . . . is a **non terminating decimal.**

We will take the approximate value of given number.

\mathtt{16.6666.\ .\ .\ \approx \ 16.67}

**(c) 13 / 7**

\mathtt{\frac{13}{7} \Longrightarrow \ 1.85714285714}

Taking approximate value.

\mathtt{1.85714285714\ \approx \ 1.86}

**(d) 8 / 9**

\mathtt{\frac{8}{9} \Longrightarrow \ 0.8888\ .\ .\ .\ .}

It’s a **non terminating decimal.**

Taking approximate value.

\mathtt{0.8888\ .\ .\ .\ \approx \ 0.89}

**(e) 50 / 2**

\mathtt{\frac{50}{2} \Longrightarrow \ 25.0}

It’s a **terminating decimal.**

**(f) 75 / 10**

\mathtt{\frac{75}{10} \Longrightarrow \ 7.5}

It’s a **terminating decimal**.

**(g) 69 / 11**

\mathtt{\frac{69}{11} \Longrightarrow \ 6.272727\ .\ .\ .}

It’s a **non terminating decimal**.

Taking approximate value;

\mathtt{6.272727\ .\ .\ .\approx \ 6.27}

**(h) 14 / 4**

\mathtt{\frac{14}{4} \Longrightarrow \ 3.5}

It’s a** terminating decimal.**

**(i) 18 / 9**

\mathtt{\frac{18}{9} \Longrightarrow \ 2.0}

It’s a **terminating decimal.**

**(j) 105 / 7**

\mathtt{\frac{105}{7} \Longrightarrow \ 15}

It’s a **terminating decimal.**

Next chapter : **Terminating and non terminating rational number**