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# Curly brackets {} around the last digits of a decimal fraction signify

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Math Expert
Joined: 02 Sep 2009
Posts: 51285
Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

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27 Nov 2016, 00:57
00:00

Difficulty:

35% (medium)

Question Stats:

62% (00:51) correct 38% (01:06) wrong based on 85 sessions

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Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is a shorthand for 0.15151515…. 10/99 is which of the following?

A. 0.{11}
B. 0.{101}
C. 0.{10}
D. 0.{09}
E. 0.{01}

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Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

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27 Nov 2016, 02:12
1
Bunuel wrote:
Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is a shorthand for 0.15151515…. 10/99 is which of the following?

A. 0.{11}
B. 0.{101}
C. 0.{10}
D. 0.{09}
E. 0.{01}

$$10/99=0.1010101010...=0.\{10\}$$

Also, there is a way to convert recurring decimal into a fraction.

Given $$a_1,a_2,...$$ are digits

$$\overline{0.\{a_1\}}=\frac{a_1}{9}$$
$$\overline{0.\{a_1 a_2\}}=\frac{\overline{a_1 a_2}}{99}$$
$$\overline{0.\{a_1 a_2 ... a_n\}}=\frac{\overline{a_1 a_2 ... a_n}}{99...9}=\frac{\overline{a_1 a_2 ... a_n}}{10^n-1}$$

For example, $$0.\{1\} = \frac{1}{9}$$
$$0.\{3\}=\frac{3}{9}=\frac{1}{3}$$
$$0.\{10\}=\frac{10}{99}$$
$$0.\{12345\}=\frac{12345}{99999}$$

$$0.\{11\}=\frac{11}{99}=\frac{1}{9}$$. Actually $$0.\{11\}=0.\{1\}$$
$$0.\{101\}=\frac{101}{999}$$
$$0.\{09\}=\frac{9}{99}=\frac{1}{11}$$
$$0.\{01\}=\frac{1}{99}$$

What about the number like $$0.12\{3\}$$?

Simply, $$0.12\{3\}=10^{-2} \times 12.\{3\}=10^{-2} \times 12\frac{3}{9}=10^{-2} \times 12\frac{1}{3}=10^{-2} \times \frac{37}{3}=\frac{37}{300}$$
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Re: Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

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27 Nov 2016, 03:28
Bunuel wrote:
Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is a shorthand for 0.15151515…. 10/99 is which of the following?

A. 0.{11}
B. 0.{101}
C. 0.{10}
D. 0.{09}
E. 0.{01}

IMO C

0.101010=x
10.1010= 100x
99x= 10
x=10/99
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Joined: 09 Sep 2013
Posts: 9206
Re: Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

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22 Feb 2018, 08:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Curly brackets {} around the last digits of a decimal fraction signify &nbs [#permalink] 22 Feb 2018, 08:10
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