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

• May 14th 2009, 11:12 AM
BabyMilo
Explain how 4/15 is equivalent to recurring decimal.
As stated in the title -
Quote:

Explain how 4/15 is equivalent to recurring decimal.
Many Thaanks!
• May 14th 2009, 11:40 AM
masters
Quote:

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.

$\frac{4}{15}=0.2\overline{6}$
• May 14th 2009, 11:44 AM
BabyMilo
no other mathematical ways? Thanks anyway!
• May 14th 2009, 08:38 PM
o_O
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.