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

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Math Expert
Joined: 02 Sep 2009
Posts: 57082
In a decimal number, a bar over one or more consecutive digits means  [#permalink]

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15 Jul 2019, 23:07
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Difficulty:

15% (low)

Question Stats:

83% (01:20) correct 17% (01:32) wrong based on 46 sessions

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

Director
Joined: 03 Jun 2019
Posts: 918
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In a decimal number, a bar over one or more consecutive digits means  [#permalink]

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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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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/

$$7.58 \overline{3} = x$$

$$100x = 758. \overline{3}$$

$$1000x = 7583. \overline{3}$$

$$900x = 6825$$

$$x = \frac{6825}{900} = \frac{91}{12}$$

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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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