Series and sequences

Find a fraction equivalent to the recurring decimal?

0.435643564356

Correct answer:

n =  44
d =  101

Step-by-step explanation:

$$\begin{gathered} a_1=0.4356 \\ q=0.0001 \\ n=a_1\mathrm{/}(1-q) \\ k=10000\cdot (1-q)=10000\cdot (1-0.0001)=9999 \\ l=10000\cdot a_1=10000\cdot 0.4356=4356 \\ s=l\mathrm{/}k=4356\mathrm{/}9999={\displaystyle \frac{44}{101}}\doteq 0.4356 \\ s=n\mathrm{/}d=44\mathrm{/}101 \\ n=44 \end{gathered}$$

$d=101$

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