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

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Math Expert
Joined: 02 Sep 2009
Posts: 53061
Which of the following fractions is equal to the repeating decimal 0.3  [#permalink]

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06 Feb 2019, 01:27
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Difficulty:

15% (low)

Question Stats:

75% (00:51) correct 25% (01:00) wrong based on 44 sessions

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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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Re: Which of the following fractions is equal to the repeating decimal 0.3  [#permalink]

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06 Feb 2019, 01:34
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

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

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Re: Which of the following fractions is equal to the repeating decimal 0.3  [#permalink]

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06 Feb 2019, 01:49
1/11 is equal to 0.090909. So if we Multiply it by it will give us answer 0.363636.

Hit for kudos if you like the answer.

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Re: Which of the following fractions is equal to the repeating decimal 0.3  [#permalink]

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13 Feb 2019, 17:39
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]

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15 Feb 2019, 17:51
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

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Re: Which of the following fractions is equal to the repeating decimal 0.3   [#permalink] 15 Feb 2019, 17:51
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