Fractions, decimals and
percentages: Rational numbers. 

3rd year of secondary education.  
Changing fractions to decimals  
A fraction can be changed into a decimal by dividing the numerator by the denominator. You can use a calculator, or see how to do it in the following window.  
The result could be:
1. A WHOLE NUMBER. For example: 72/9=8. This is the case when the
numerator is a multiple of the denominator.
3. A PURE RECURRING DECIMAL  For example: 4/11=0.36363636... The
decimal numbers form a pattern that is repeated indefinitely after the
decimal point. Look at these different examples in the window. 
Rational numbers  
We have just seen,
in the section above, how we can get four different types of numbers when we
divide a fraction (a whole number, a terminating decimal or a pure or mixed
recurring decimal). All of these numbers could be said to fall into the category
of recurring decimals, as a whole number, such as 4, could be
written as 4.00000... and a terminating decimal, such as 0.25, could be written
as 0.250000...
Therefore, we could say that any fraction can be expressed as a recurring decimal. We can also say that the opposite is true, i.e. that any recurring decimal can be expressed as a fraction. From now on we shall refer to these numbers as rational numbers. To sum up:
ANY NUMBER THAT CAN BE EXPRESSED
AS A FRACTION IS KNOWN AS A RATIONAL NUMBER We have just seen how we can get four different types of numbers when we divide a fraction. All of these numbers are RATIONAL. We are going to refer to this group of numbers with the letter Q. We can classify the set Q of RATIONAL NUMBERS as follows: 
Ángela Núñez Castaín  
Spanish Ministry of Education. Year 2001  
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