As stated in the title -Many Thaanks!Explain how 4/15 is equivalent to recurring decimal.
Hi BabyMilo,
Let's do the long division on this thing.
As you can see, the 6 will continue to repeat because the remainder will always be 10 as we continue to divide.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
$\displaystyle \frac{4}{15}=0.2\overline{6}$
Sure there is.
Let $\displaystyle S = 0.266\overline{6}$.
Multiply both sides by 100: $\displaystyle 100S = 26.66\overline{6}$
Subtract by the first line: $\displaystyle 99S = 26.400..$
So: $\displaystyle S = \frac{26.4}{99} \cdot \underbrace{{\color{red}\frac{5}{5}}}_{\displaysty le =1} = \frac{132}{495}$
Reduce the final fraction and you'll get what you want.