What is the 2015th decimal number in the division 2015 by 7

[Natasha1]

What is the 2015th decimal number in the division 2015 by 7?

This is how I did it but is there an simpler way of showing this...

I did 2015/7 = 287.857142 857142 857142 857142 ...

As we have a recurring decimal for the numbers 857142, I divided 2015 by 6 which gives me a non finite answer so I then divided 2016 by 6 = 336. Therefore I concluded that the 2016th number must be an 8 and to answer the question which is 2015th number it must be the preceding number in the recurring pattern so it's 2.

Am I correct please and could anyone explain a clearer or simpler way, if it exist. Thank you :)

 

[BvU]

By you reasoning, what is the 24th number ?

 

[Natasha1]

As there are 6 numbers in the sequence 857142 and 24/6 = 4 then the 24th number is 2

 

[BvU]

So what about the 2016 th number ?

 

[Natasha1]

Well it must be 2 as 2016/24 = 84

 

[BvU]

In post #1

to answer the question which is 2015th number it must be the preceding number in the recurring pattern so it's 2

 

[vela]

so I then divided 2016 by 6 = 336. Therefore I concluded that the 2016th number must be an 8

As there are 6 numbers in the sequence 857142 and 24/6 = 4 then the 24th number is 2

Do you see the contradiction in your two results?