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Recurring decimals

"Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

What are the subsequent digits of the decimal? -:smile:
(edited 8 years ago)
Reply 1
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Zacken
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Original post by RosaA
"Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

What are the subsequent digits of the decimal? -:smile:


That's quite weird. Taken at face value it means: 5.237131313131313131313131313131…5.237131313131313131313131313131\ldots
Reply 2
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RosaA
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Original post by Zacken
That's quite weird. Taken at face value it means: 5.2371313131313131313131313131…5.2371313131313131313131313131\ldots


Definitely strange.

I wasn't sure about what to do with the 7 ... thanks :biggrin:
Reply 3
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Zacken
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Original post by RosaA
Definitely strange.

I wasn't sure about what to do with the 7 ... thanks :biggrin:


I think I'm right, if I am, you're welcome. If not... :lol: :colondollar:
(edited 8 years ago)
Reply 4
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RosaA
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Original post by Zacken
I think I'm right, if I am, you're welcome. If not... :lol: :colondollar:


Feeling extremely confident that the answer will be correct.... :colonhash: *laughs*
Reply 5
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Zacken
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Original post by RosaA
Feeling extremely confident that the answer will be correct.... :colonhash: *laughs*


The answer is quite ugly regardless of whether I include the 7 or not... :colondollar:
(edited 8 years ago)
Original post by RosaA
"Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

What are the subsequent digits of the decimal? -:smile:


If there is a dot above the 3 and 1, it means the recurring part is 371

i.e.

5.2371371371371371
Reply 7
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Zacken
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*bows out in shame*
Reply 8
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RosaA
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Original post by Student403
If there is a dot above the 3 and 1, it means the recurring part is 371

i.e.

5.2371371371371371


See, that's what I originally thought... :h:
The dots are above 3 and 1 which means that they cover that region...

Thank you!! :biggrin:
Reply 9
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Zacken
22
Original post by RosaA
See, that's what I originally thought... :h:
The dots are above 3 and 1 which means that they cover that region...

Thank you!! :biggrin:


Sorry. :colondollar:
Reply 10
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RosaA
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Original post by Zacken
Sorry. :colondollar:


All is forgiven :u:
Original post by Zacken
*bows out in shame*


Don't worry about it lol
Original post by RosaA
"Express the recurring decimal 5.2371 (3 and 1are recurring) as a fraction"

What are the subsequent digits of the decimal? -:smile:


5.2371371371... = 5.2 + 0.0371371371... = 5.2 + 0.371371371.../10.

Now, let x = 0.371371371..., so 1000x = 371.371371...
Thus 1000x - x = 371.371371... - 0.371371... = 371 -> 999x = 371 -> x = 371/999.

Hence the original number is 5.2 + (371/999)/10 = 5.2 + 371/9990 = 26/5 + 371/9990 = 52319/9990.
Reply 13
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RosaA
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Original post by HapaxOromenon2
5.2371371371... = 5.2 + 0.0371371371... = 5.2 + 0.371371371.../10.

Now, let x = 0.371371371..., so 1000x = 371.371371...
Thus 1000x - x = 371.371371... - 0.371371... = 371 -> 999x = 371 -> x = 371/999.

Hence the original number is 5.2 + (371/999)/10 = 5.2 + 371/9990 = 26/5 + 371/9990 = 52319/9990.


Thank you for explaining the methodology -even though I didn't need help on that aspect of it! :biggrin:
I just wanted to clarify what the subsequent digits where of the decimal but thank you for the help anyway.
i have this question can u say what u got for the fraction

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