Question

How can you write 1.2244444444444444.... as a fraction?

Answer 1

`1.2244444... = 1102/900 = 551/450`

Explanation:

If you see a single repeating digit, try multiplying by `9` first:

`1.2244444... * 9 = 11.02`

To make this into an integer just multiply by `100`

`11.02 * 100 = 1102`

So:

`1.2244444... * 900 = 1102`

Divide both sides by `900` to get:

`1.2244444... = 1102 / 900`

Actually both `1102` and `900` are even, so divide top and bottom by `2` to get:

`1.2244444... = 551 / 450`

Incidentally, I don't know if it's still popular, but there's a notation for repeating decimals, where you place a dot or dots above digits as follows:

`1.22dot(4)` to mean `1.2244444...`

Or if you have a repeating pattern of more than one digit, use a dot to mark each end of the repeating pattern, so:

`1/7 = 0.dot(1)4285dot(7)`

Perhaps you just did not know how to get Socratic to display this.