Write two-ninths as a recurring decimal.
We recall that the line in a fraction means divide. This means that we can convert two-ninths into a decimal by dividing two by nine. As nine does not divide into two, we can add a decimal point and some zeros after it. We could add any number of zeros after the decimal point. We are told that our answer will be a recurring decimal. This is a decimal that repeats forever.
As nine does not divide into two, we need to carry the two to the tenths column. We keep the decimal point in the same place. 20 divided by nine is equal to two remainder two as two multiplied by nine is 18. We carry the two to the hundredths column and repeat the process. Once again, we get two remainder two. This pattern will continue indefinitely. The only number that is repeating is the two. So, we only need to write this once. We put a bar or a dot above this number.
Two-ninths written as a recurring decimal is 0.2 recurring. This result leads us to a pattern that is worth remembering. One-ninth is equal to 0.1 recurring. We have just worked out that two-ninths is equal to 0.2 recurring. This pattern continues all the way up to eight-ninths, which is 0.8 recurring. When our denominator is nine, the recurring decimal will be the numerator.