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

Jun 28, 2015

$1.2244444 \ldots = \frac{1102}{900} = \frac{551}{450}$

#### Explanation:

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

$1.2244444 \ldots \cdot 9 = 11.02$

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

$11.02 \cdot 100 = 1102$

So:

$1.2244444 \ldots \cdot 900 = 1102$

Divide both sides by $900$ to get:

$1.2244444 \ldots = \frac{1102}{900}$

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

$1.2244444 \ldots = \frac{551}{450}$

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:

$1.22 \dot{4}$ to mean $1.2244444 \ldots$

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

$\frac{1}{7} = 0. \dot{1} 4285 \dot{7}$

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