Fractions can be expressed as decimal numbers, which can help us better understand their values on the number line. Let’s look at an example of this:
The fraction can also be written as . On a number line, is halfway between and .
The fraction is and is .
Decimal numbers can either terminate after a finite number of decimal places or recur (repeat) indefinitely.
Some fractions, when converted to decimal form, have a finite number of decimal places. For example:
Other fractions, when converted to decimal form, have an infinitely repeating pattern of digits. For example:
To show a repeating pattern, a dot is placed above the repeating digit or group of digits.
Every fraction is a rational number, which can be expressed in the form , where and are integers and . Rational numbers include integers, as they can be written as fractions with a denominator of 1 (e.g., , , ).
On the other hand, irrational numbers cannot be expressed as fractions. Their decimal representations go on forever without repeating. Some examples of irrational numbers are , , , , .
In these examples, the overline notation indicates which digits or groups of digits are repeating in the decimal representation of the fraction.