5/9 is an amount that cannot be exactly represented in the decimal system because 9 will not go into 10 evenly.
There is a trick you can use to indicate the correct value directly. Start to write the number, but after the decimal write the repeating portion only once - then draw a bar over the repeating portion. This indicates the full answer more specifically than the more common use of 0.555...
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repeating decimal
A repeating decimal is usually shown with a bar over the decimal that is repeated
29/7 as a repeating decimal is 4.'142857' repeating '142857'
0.3333 repeating
It is: 5.'63' repeating '63'