Fraction to decimal infinite

Determine which digit is at 1000th place after the decimal point in the decimal expansion of the fraction 9/28.

Correct answer:

d =  4

Step-by-step explanation:

$$\begin{gathered} 9\mathrm{/}28={\displaystyle \frac{9}{28}}=0.3214285714285714285714285714285714285714285714285714285714285714\dots \\ p=142857 \\ {p}_1=1 \\ {p}_2=4 \\ {p}_3=2 \\ {p}_4=8 \\ {p}_5=5 \\ {p}_6=7 \\ {D}_1=(1000-2)\mathrm{/}6={\displaystyle \frac{499}{3}}=166\frac{1}{3}\doteq 166.3333 \\ {n}_1=998-166\cdot 6=2 \\ i=\mathrm{m}\mathrm{o}\mathrm{d}(998,6)=2 \\ d=p[i] \\ d=p_2=4 \end{gathered}$$

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Showing 4 comments:

Math student

this suck's so much like are

3 months ago  4 Likes Like

Math student

I don't know

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Math student

This is really cool

1 month ago  Like

Math But Awkward

i don't like this but thanks for making it

25 days ago  Like

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