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A3. Fractions : recurring decimals. A recurring decimal is one whose digits after the decimal point do not end but repeat the same sequence for ever. These are all recurring decimals: 0.121212... 0.111111... 0.74357435... Recurring decimals are also known as repeating decimals or periodic decimals. The number of digits in the repeating pattern is called the period. So: 0.121212... has a period of 2 0.74357435... has a period of 4 Any repeating decimal can be converted to a fraction. To do this you need to see how the decimal can be written as an infinite geometric series. Here is an example of how you do it. 0.363636...=0.36 + 0.0036 + 0.000036 + ... This infinite sequence is an example of an infinite geometric series. It has a first term, a=0.36=36/100=9/25 and a constant ratio, r=0.01=1/100. In your Advanced Level course, you will meet the following formula for the sum of an infinite geometric series: S=a/(1-r) So, in the above case, 0.363636...=9/25/(1-1/100)=9/25 x 100/99=900/2475=4/11 Convert the decimal to an exact fraction and check your answer. Press the button to get started. as an exact fraction: /