 in this video we're going to look at recurring decimals. Recurring decimals repeat forever and ever and ever. To save us having to write all of the repeating numbers we can place a dot above the number or numbers that repeat. So that is one-third written as a recurring decimal and we can write this number as 0.123 with a dot above the first 1, 2 and 3. If all the decimal places don't repeat just put a dot above the ones that do. All recurring decimals can be written as fractions and writing them as fractions is even better than using the dots. In this video we're going to look at how to write recurring decimals as fractions. Let's jump straight in with an example. We need to start by forming the two equations. Let x equal 0.8888 and so on. We now multiply both sides by 10 or 100 or 1000 or maybe even 10,000 so that we move the repeating number or numbers so the 8 to the left of the decimal place. You will see that this is really important in later examples. So here we multiply both sides by 10 and we get 10x equals 8.888 and so on. So the repeating 8 has moved to the left of the decimal place. Now we subtract x from 10x to eliminate the repeating 0.888 part. So we get 10x minus x equals 8.888 minus 0.888. So 9x equals 8, a little bit of rearranging. Divide both sides by 9 and x equals 8 divided by 9. We can check that on our calculator. 8 divided by 9 equals 0.888 recurring. So we know we're right. So let's look at a different example. Remember how earlier I said we may multiply by 10, 100, 1000 or maybe even 10,000 to move the repeating numbers to the left of the decimal place? We're going to see what I mean by that. As always, let x equal 0.56787878. Be careful that it is only the 78 that's repeating. So we need to multiply by 10,000 so that we move the repeating 7.8 to the left of the decimal place. So 10,000x equals 5678.787878 recurring. But our decimals don't match up. If we subtract they won't eliminate. So we need to multiply also by 100 to match up the decimal places. So 100x equals 56.787878 recurring. And now our repeating parts match up so we can eliminate the decimal places. Now we can do 10,000 minus 100 equals 5678.78 minus 56.78. So 9,900x equals 5678 take away 56 which equals 5,622. So a little bit of rearranging. Divide both sides by 9,900 and we get x equals 5,622 divided by 9,900. And again we can check this on our calculator. So give this question a go yourself. You may need to multiply by 10, 100, 1,000 or maybe even 10,000. Just be careful that the 7 is repeating but the 2 isn't. Pause the video, work out the answer and click play when you're ready to check. Did you get it right? 5 18ths. So what about this question? Pause the video, work it out and click play when you're ready. Did you get it right? 14 over 225. So there you have turning recurring decimals into fractions. Remember that this is the method and you may need to multiply by 10, 100, 1,000 or maybe even 10,000.