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If m and n are integers, what is the smallest possible value

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If m and n are integers, what is the smallest possible value [#permalink] New post 22 May 2018, 08:36
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If m and n are integers, what is the smallest possible value of integer m, if m/n = 0.36363636..........?

[Reveal] Spoiler:
4


src: orbit test prep
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Re: If m and n are integers, what is the smallest possible value [#permalink] New post 24 May 2018, 21:57
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Since the digits after decimal point is repeating in a pair of 36 when we multiply \(\frac{m}{n}\) by 100 we get 36.363636.....

Therefore, \(100 * \frac{m}{n}- \frac{m}{n} = 36\)
or, \(99 \frac{m}{n} = 36\)
or, \(99m = 36n\)
The ans requires the value of m such that m/n is reduced to its lowest fraction
Therefore when dividing both sides by 9 we get,
\(11m = 4n\)
or, \(\frac{m}{n}\) = \(\frac{4}{11}\)
Hence, m = 4
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Re: If m and n are integers, what is the smallest possible value   [#permalink] 24 May 2018, 21:57
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If m and n are integers, what is the smallest possible value

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