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In a decimal number, a bar over one or more consecutive digits means

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In a decimal number, a bar over one or more consecutive digits means  [#permalink]

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New post 15 Jul 2019, 23:07
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In a decimal number, a bar over one or more consecutive digits means that the pattern of digits under the bar repeats without end. What fraction is equal to \(7.58 \overline{3}\) ?

A. \(\frac{91}{3}\)

B. \(\frac{91}{4}\)

C. \(\frac{91}{6}\)

D. \(\frac{91}{9}\)

E. \(\frac{91}{12}\)

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Re: In a decimal number, a bar over one or more consecutive digits means  [#permalink]

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New post 15 Jul 2019, 23:16
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Of all the answer choices, only \(\frac{91}{12}\) has a quotient of 7

Answer is (E)
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In a decimal number, a bar over one or more consecutive digits means  [#permalink]

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New post 16 Jul 2019, 00:57
Bunuel wrote:
In a decimal number, a bar over one or more consecutive digits means that the pattern of digits under the bar repeats without end. What fraction is equal to \(7.58 \overline{3}\) ?

A. \(\frac{91}{3}\)

B. \(\frac{91}{4}\)

C. \(\frac{91}{6}\)

D. \(\frac{91}{9}\)

E. \(\frac{91}{12}\)


\(Let x =7.58\overline{3}\)
\(Then 10x = 75.83\overline{3}\)
10x-x =9x = 68.25
\(x=\frac{68.25}{9}=\frac{273}{9*4}=\frac{91}{12}\)

IMO E
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Re: In a decimal number, a bar over one or more consecutive digits means  [#permalink]

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New post 16 Jul 2019, 02:42
Bunuel wrote:
In a decimal number, a bar over one or more consecutive digits means that the pattern of digits under the bar repeats without end. What fraction is equal to \(7.58 \overline{3}\) ?

A. \(\frac{91}{3}\)

B. \(\frac{91}{4}\)

C. \(\frac{91}{6}\)

D. \(\frac{91}{9}\)

E. \(\frac{91}{12}\)


Check this post first: https://www.veritasprep.com/blog/2014/0 ... fractions/

\(7.58 \overline{3} = x\)

\(100x = 758. \overline{3}\)

\(1000x = 7583. \overline{3}\)

\(900x = 6825\)

\(x = \frac{6825}{900} = \frac{91}{12}\)

Answer (E)
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Re: In a decimal number, a bar over one or more consecutive digits means   [#permalink] 16 Jul 2019, 02:42
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