Number must be between 0 and 1

Numerator Range: 0-999

Denominator Range: 1-1000

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This is a little toy to help you understand how decimal notation works.

We divide the number line up into 10 closed intervals and give each of them a label. A closed interval is just a set of numbers between two points where both of the endpoints are included. For example, the interval labeled 5 includes all of the points between 5/10 and 6/10, as well as 5/10 and 6/10 themselves.

The red line represents the number for which we're trying to find a decimal. For each digit, we simply look at which interval contains our number and add its label to our decimal. Then we zoom in on that interval and repeat the process.

Since we're using closed intervals, each interval shares its endpoints with its neighbors. This means that it's possible for our number to be in two different intervals at once. As a result, some numbers have two different decimal representations. Can you figure out which numbers have two decimal representations in general?

Click here for a longer explanation without the fancy animations.