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Which of the following fractions is equal to the repeating decimal 0.3

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Bunuel
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Which of the following fractions is equal to the repeating decimal 0.3 [#permalink] New post   06 Feb 2019, 02:27
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Which of the following fractions is equal to the repeating decimal 0.3636...?


A. 1/275

B. 2/55

C. 4/99

D. 4/11

E. 4/9
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D
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Re: Which of the following fractions is equal to the repeating decimal 0.3 [#permalink] New post   06 Feb 2019, 02:34
Bunuel wrote:
Which of the following fractions is equal to the repeating decimal 0.3636...?


A. 1/275

B. 2/55

C. 4/99

D. 4/11

E. 4/9


Scan the answer choices

4/11 = 0.3636............

D is the correct answer.
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Re: Which of the following fractions is equal to the repeating decimal 0.3 [#permalink] New post   06 Feb 2019, 02:49
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1/11 is equal to 0.090909. So if we Multiply it by it will give us answer 0.363636.

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Re: Which of the following fractions is equal to the repeating decimal 0.3 [#permalink] New post   13 Feb 2019, 18:39
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Recurring terminal to fractions:

3636... two digits [36]

\(36/99 = 4/11\)
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Re: Which of the following fractions is equal to the repeating decimal 0.3 [#permalink] New post   15 Feb 2019, 18:51
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Bunuel wrote:
Which of the following fractions is equal to the repeating decimal 0.3636...?


A. 1/275

B. 2/55

C. 4/99

D. 4/11

E. 4/9


We see that 0.3636 is between 1/3 and 2/5.

Looking at the answer choices 1/275. 2/55 and 4/99 are too small, and since 4/9 is close to 1/2, we see that the correct answer must be 4/11.

Alternate solution:

We see that the decimal is a repeating decimal between 0 and 1 and the digits 36 repeat indefinitely right after the decimal point. In that case, it means the numerator is 36 and the denominator is 99, so the fraction is 36/99 = 4/11.

Alternate Solution:

If we let x = 0.3636… , then 100 x = 36.3636…

Subtracting the first equation from the second, we have

99x = 36

x = 36/99 = 4/11

Answer: D
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Re: Which of the following fractions is equal to the repeating decimal 0.3 [#permalink]
15 Feb 2019, 18:51
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