What Is the Longest Repeating Decimal?

By Charlie Kasov

The longest repeating decimal doesn't actually exist in the most literal terms. Find out about the longest repeating decimal with help from a math expert in this free video clip.


Hi, I'm Charlie Kasov, and this is what is the longest repeating decimal, and the answer to that is there is no one longest repeating decimal. Any repeating decimal that is infinite is going to go on to infinity, so all of them would be equally long. For example, if we have two-thirds, that equals .666 on and and on, and we'd say point six repeating. So, we could say one-third is point three repeating. You might have been taught to change this to .33, or .34, but they're gonna go onto infinity. So the important thing to know with repeating decimals is when to put the line on, and then stop. For example, with one-eleventh, we're gonna call that .09, and the bar goes over both of the numbers because it will go .090909 whereas three will just keep going. So I'm Charlie Kasov, and you've learned the answer to what is the longest repeating decimal.

About the Author

Charlie Kasov has been tutoring high school mathematics since 2004. He is qualified to teach several math subjects, including geometry, algebra, trigonometry and probability.