# Math Help - Explain how 4/15 is equivalent to recurring decimal.

1. ## Explain how 4/15 is equivalent to recurring decimal.

As stated in the title -
Explain how 4/15 is equivalent to recurring decimal.
Many Thaanks!

2. Originally Posted by BabyMilo
As stated in the title - Many Thaanks!
Hi BabyMilo,

Let's do the long division on this thing.

Code:

0  .  2   6   6    6   6
------------------------
15 | 4  .  0   0   0    0   0
0
----------
4     0
3     0
---------
1    0   0
9   0
-----------
1   0   0
9   0
----------
1   0
As you can see, the 6 will continue to repeat because the remainder will always be 10 as we continue to divide.

$\frac{4}{15}=0.2\overline{6}$

3. no other mathematical ways? Thanks anyway!

4. Sure there is.

Let $S = 0.266\overline{6}$.

Multiply both sides by 100: $100S = 26.66\overline{6}$

Subtract by the first line: $99S = 26.400..$

So: $S = \frac{26.4}{99} \cdot \underbrace{{\color{red}\frac{5}{5}}}_{\displaysty le =1} = \frac{132}{495}$

Reduce the final fraction and you'll get what you want.