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

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Homework Help Overview

The discussion revolves around finding the 2015th decimal digit in the division of 2015 by 7, which results in a recurring decimal. Participants explore the nature of the decimal expansion and the implications of the recurring sequence.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to determine the 2015th digit by analyzing the recurring decimal pattern and suggests a method involving division by the length of the repeating sequence. Other participants question the reasoning and explore related positions in the sequence, such as the 24th and 2016th digits.

Discussion Status

The discussion is ongoing, with participants raising questions about the original poster's reasoning and identifying potential contradictions in the results. There is an exploration of different interpretations of the recurring sequence and its implications for identifying specific decimal places.

Contextual Notes

Participants are working within the constraints of identifying decimal places in a recurring sequence, and there is a focus on the implications of the periodic nature of the decimal expansion.

Natasha1
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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 :)
 
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By you reasoning, what is the 24th number ?
 
As there are 6 numbers in the sequence 857142 and 24/6 = 4 then the 24th number is 2
 
So what about the 2016 th number ?
 
Well it must be 2 as 2016/24 = 84
 
In post #1
Natasha1 said:
to answer the question which is 2015th number it must be the preceding number in the recurring pattern so it's 2
 
Natasha1 said:
so I then divided 2016 by 6 = 336. Therefore I concluded that the 2016th number must be an 8
Natasha1 said:
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?
 

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