YOU ARE LEARNING:
A recurring decimal follows a pattern after the decimal point, and it is important to be able to convert recurring decimals into fractions.
A recurring decimal is a decimal which follows some kind of pattern.
Is this a recurring decimal?
Recurring decimals can always be written as fractions.
Let's try converting 0.2222...into a fraction.
Let 0.2222... equal x
Take away x from 10x
2.222..−0.222...=2. This means we now have a whole number!
We started with 10x=2.222... and subtracted x=0.222...
Make x the subject
What is 0.33333... as a fraction in its simplest form?
What is 0.55555... as a fraction in its simplest form?
There are also recurring decimals where the pattern repeats every 3 digits such as 0.357357357....
Write 0.357357357... as a fraction in it's simplest form.
Multiply x by 1000
This means that the repeating unit is ahead of the decimal point, and leaves us with 357.357357...
Subtract x=0.357... from 1000x=357.357...
Express this as a fraction
After subtracting, we have 999357
Simplify the fraction
There is a common factor of 3! 999357=333119
Great work! 👍
The final answer is 333119
What is 0.363636... as a fraction in its simplest form?
What is 0.757575... as a fraction in its simplest form?
Another type of recurring decimal you might come across is 0.211111... In this case, we perform the same process, but this time subtract 10xfrom 100x to remove the repeating unit.
What is 0.17777... as a fraction?
What is 0.288888... as a fraction?