+0

# Converting 1-digit repeating decimals to fractions

0
2179
5
Rewrite as a simplified fraction.

1.5¯=?
Mar 17, 2014

#1
+121056
+9
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.
Mar 17, 2014
#2
+32557
0
boo09:

Rewrite as a simplified fraction.

1.5¯=?

If the 5 recurs forever then:
Recurring.PNG
Mar 17, 2014
#3
+114485
0
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
Mar 18, 2014
#4
+121056
+8
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!!
Mar 18, 2014
#5
+32557
0
Well done Melody. My first step was, indeed, an unnecessary complication!
Mar 18, 2014