The division process

An alternative method is to divide the numerator of the fraction by its denominator as shown below. The algorithm is an extension of the division algorithm for whole numbers.

Example 2

Convert \(\dfrac{743}{8}\) to a decimal using the division process.

Solution

This can be done by several methods, but the first step for each of these methods is to observe that

\(\dfrac{743}{8}\) = 743 ÷ 8

The short division algorithm can be adapted.

We set out 743 ÷ 8 as shown below:

We have had to add trailing zeros.

The number 92.875 is a terminating decimal. The division process terminates.

By using a technique similar to that of the example above it can be shown that \(\dfrac{1}{3}\) = 0.33333… The digit 3 is obtained endlessly as new trailing zeros are added and the division algorithm continued. The decimal 0.3333… is called a recurring decimal. These will be discussed later in this module.

We can determine which fractions are terminating and which fractions are recurring decimals by examining the denominator of the fraction.