Notation for recurring decimals

Sometimes when you divide into a number there is a recurring decimal

Because a third has an infinite amount of 0.3's it is a recurring decimal

$1/3=0.333333.......$ recurring

This can be written as

$1/3=0.dot3$
or
$1/3=0.bar3$

The dot or dash means that the $3$ is repeated indefinitely.

But repeated decimals can occur in a pattern.

If 2 recurring symbols are shown, it means the numbers between the symbols are repeated

This can be written as

$4/7=0.dot5\714dot2$ or $4/7=0.bar5\714bar2$

This is written with a dot over the first and last part of the recurring pattern.

Example 1

Put the following fraction in recurring decimal form $22/7$

If 2 recurring symbols are shown, it means the numbers between the symbols are repeated

Written out recurring decimal

Example 2

What does $1.dot5$ mean?

$1.dot5$ means $1.5555555$ repeating

Example 3

Write $22.520101010$ as a recurring decimal using dots

This equals $22.520dot1dot0$

Example 4

Express $4/9$ as a decimal

0.4444 can also be a recurring decimal but make sure it has the dot or dash above the repeated number

$4/9=0.4444$ recurring

$4/9=0.dot4$