Decimals to common fractions
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How to convert decimal fractions to common fractions.

This topic is part of the TCS FREE high school mathematics 'How-to Library'. It shows you how to convert decimal fractions to common fractions.
(See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Algematics software. Click here for instructions.

 

Download the free support file... We have created an Algematics document containing the completed example from this topic. It also includes practice exercises to improve your skills.

File name:  'Decimals to common fractions.alg'   File size: 3kb
Click here to download the file.

If you choose 'Open this file from its current location', then Algematics should open the document immediately. If not, try the other option: 'Save this file to disk', then run Algematics and choose the 'Open' command from the 'File' menu. Locate the saved file and open it. If you do not yet have Algematics installed on your computer, click here for instructions.

Method:

Use the place value of the last digit after the decimal point to write the decimal as a fraction.

For example, in the decimal fraction: 23.56, the last digit, 6, is in the hundredths place.
So the entire number can be expressed in hundredths as follows:

           

To demonstrate this procedure with more steps, enter the decimal number into Algematics as the sum of units, tenths, hundredths and so on, like this:

           

We will use this example in the steps below.

Step 1 Enter the data

Click  and type your expression into the maths box in the data entry dialog box.

If the ‘EMPTY’ message is not displayed between the blue buttons, click the  button until the message: ‘INSERT’ appears.  If required, use the ‘ / ’ symbol for divide.

 

       Maths...

   23.56 = 23 + 5/10 + 6/100

 

 

 

and then click

Step 2 Put over a common denominator

Click the  (common denominator) button to put these terms over a common denominator, like this:

           

Step 3 Simplify

Click the  (simplify) button several times until a single fraction is obtained. Clicking  again will reduce the fraction to its lowest terms, if possible.

23.56   simplifies to:  
 

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