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# Recurring decimals

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

What are the subsequent digits of the decimal? -
2. (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? -
That's quite weird. Taken at face value it means:
3. (Original post by Zacken)
That's quite weird. Taken at face value it means:
Definitely strange.

I wasn't sure about what to do with the 7 ... thanks
4. (Original post by RosaA)
Definitely strange.

I wasn't sure about what to do with the 7 ... thanks
I think I'm right, if I am, you're welcome. If not...
5. (Original post by Zacken)
I think I'm right, if I am, you're welcome. If not...
Feeling extremely confident that the answer will be correct.... *laughs*
6. (Original post by RosaA)
Feeling extremely confident that the answer will be correct.... *laughs*
The answer is quite ugly regardless of whether I include the 7 or not...
7. (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? -
If there is a dot above the 3 and 1, it means the recurring part is 371

i.e.

5.2371371371371371
8. *bows out in shame*
9. (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...
The dots are above 3 and 1 which means that they cover that region...

Thank you!!
10. (Original post by RosaA)
See, that's what I originally thought...
The dots are above 3 and 1 which means that they cover that region...

Thank you!!
Sorry.
11. (Original post by Zacken)
Sorry.
All is forgiven
12. (Original post by Zacken)
*bows out in shame*
13. (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? -
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.
14. (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!
I just wanted to clarify what the subsequent digits where of the decimal but thank you for the help anyway.

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