Converting 1-digit repeating decimals to fractions

If I read your question correctly, you'd like to convert a repeating mixed number like 1.5555..... to a fraction.

Here's the way to do this.

Suppose we have 1.5555.

Forget the whole number part - we can add that back later.

Write the rest without the decimal....i.e., 5555.

Put this over a denominator that has the same number of 9's as the number of digits in the decimal part....i.e., 9999.

So we have 5555 / 9999.

Check this with your calculator...I think you'll get .5555.

Add the 1 back to the front of the fraction. to get the mixed number = 1 + (5555/9999).

That's it.

boo09:

Rewrite as a simplified fraction.

1.5¯=?

If the 5 recurs forever then:
Recurring.PNG

boo09:

Rewrite as a simplified fraction.

1.5¯=?

Thanks guy but I can't help myself.
My way is more versatile than CPhill's and easier than Alan's. That's what I think anyway.
Besides it was good LaTex practice.

140318 repeater decimal to fraction.JPG

Thanks, Melody and Alan........Both of your methods are certainly more "mathematical" than mine!!!

It's always good to learn a new method of doing things!!

Well done Melody. My first step was, indeed, an unnecessary complication!