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`