The fraction can also be written as . On a number line is halfway between and .
The fraction is and is .
All fractions can be written as a decimal number. The decimal form of a fraction will either stop after a finite number of decimal or will recur (periods); it keeps repeating.
But the fraction is , the never ends, but keeps going forever.
is also , here the never stops.
It is important to be able to write functions as their decimal equivalent.
Every fraction has the form where and are integers.
. We also call the fraction rational.
But numbers exist which cannot be written as fractions, their decimals go on forever without repeating (recur).
Another example of such a number is . There are many that exist, which we call irrational numbers.
are other examples of irrational numbers.
When we take all types of numbers, we simply call them real numbers. So the real numbers include integers, fractions and also the irrational numbers.
The integers are also rational numbers because they can all be written in the form a/b with b=1.
Thus and so on.
The fraction which in decimal form is can be written as
With the dots placed on top of the group of numbers that repeat.
will be written as and as ̇