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Bunuel
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A bar over a sequence of digits in a decimal indicates that the sequen 10 Mar 2023, 08:45
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35% (medium)

Question Stats:

68% (01:12) correct 32% (01:27) wrong based on 165 sessions

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A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. Which of the following fractions is equivalent to \(0.\overline{12}\) ?

A. 3/25

B. 4/33

C. 109/900

D. 11/90

E. 12/90
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B
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MimRahman452
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A bar over a sequence of digits in a decimal indicates that the sequen 10 Mar 2023, 09:20
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fraction = ( bar digits-non bar digits)/ 99999..... [ 9 for each bar digits after decimal & 0 for each non bar digits after decimal]
so ,
0.{bar 12} = (12-0)/99
=12/99
=4/33
ans.: B
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A bar over a sequence of digits in a decimal indicates that the sequen 10 Mar 2023, 09:21
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fraction = ( bar digits-non bar digits)/ 99999..... [ 9 for each bar digits after decimal & 0 for each non bar digits after decimal]
so ,
0.{bar 12} = (12-0)/99
=12/99
=4/33
ans.: B
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A bar over a sequence of digits in a decimal indicates that the sequen 10 Mar 2023, 11:27
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Bunuel
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. Which of the following fractions is equivalent to \(0.\overline{12}\) ?

A. 3/25

B. 4/33

C. 109/900

D. 11/90

E. 12/90
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\(\frac{1}{3} = 0.\overline{03}\)

Hence, \(\frac{4}{3} = 0.\overline{12}\), Answer must be (B)
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A bar over a sequence of digits in a decimal indicates that the sequen 29 Dec 2023, 19:48
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Abhishek009
Bunuel
A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. Which of the following fractions is equivalent to \(0.\overline{12}\) ?

A. 3/25

B. 4/33

C. 109/900

D. 11/90

E. 12/90

\(\frac{1}{3} = 0.\overline{03}\)

Hence, \(\frac{4}{3} = 0.\overline{12}\), Answer must be (B)
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How do you determine that 1/33 = 0.03 [overline]?
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Khwarizmi
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A bar over a sequence of digits in a decimal indicates that the sequen 29 Dec 2023, 19:59
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MimRahman452
fraction = ( bar digits-non bar digits)/ 99999..... [ 9 for each bar digits after decimal & 0 for each non bar digits after decimal]
so ,
0.{bar 12} = (12-0)/99
=12/99
=4/33
ans.: B
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Can you please elaborate on this answer? I'm having a hard time solving this problem. Why do we specifically divide by 9 for each bar digit after the decimal and 0 for each non-bar digit after the decimal?

Bunuel feel free to chime in if you have a wonderful explanation as you usually do.
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Bunuel
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A bar over a sequence of digits in a decimal indicates that the sequen 30 Dec 2023, 01:19
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Khwarizmi
MimRahman452
fraction = ( bar digits-non bar digits)/ 99999..... [ 9 for each bar digits after decimal & 0 for each non bar digits after decimal]
so ,
0.{bar 12} = (12-0)/99
=12/99
=4/33
ans.: B

Can you please elaborate on this answer? I'm having a hard time solving this problem. Why do we specifically divide by 9 for each bar digit after the decimal and 0 for each non-bar digit after the decimal?

Bunuel feel free to chime in if you have a wonderful explanation as you usually do.
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Check Math: Number Theory. Hope it helps.
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misterteddy
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A bar over a sequence of digits in a decimal indicates that the sequen 31 Jan 2025, 23:05
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Quote:
fraction = ( bar digits-non bar digits)/ 99999..... [ 9 for each bar digits after decimal & 0 for each non bar digits after decimal]
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The genral form must be (ALL digits - non bar digits), not (BAR digits - non bar digits).
If you wonder why, please check the explanation in the attachment.
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File comment: Explanation from DeepSeek
Screenshot 2025-02-01 at 13.03.52.png
Screenshot 2025-02-01 at 13.03.52.png [ 138.45 KiB | Viewed 1211 times ]

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A bar over a sequence of digits in a decimal indicates that the sequen 29 Mar 2025, 02:36
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Let x = 0.121212...
Multiply by 100 to shift decimal:
100x = 12.121212...
Subtract:
100x - x = 12.121212... - 0.121212...
99x = 12
Solve:
x = 12/99 = 4/33
Answer: B (4/33)
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