GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 17:54

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58445
Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

### Show Tags

27 Nov 2016, 01:57
00:00

Difficulty:

35% (medium)

Question Stats:

57% (00:51) correct 43% (01:10) wrong based on 94 sessions

### HideShow timer Statistics

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}

_________________
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1333
Location: Viet Nam
Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

### Show Tags

27 Nov 2016, 03:12
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, $$0.12\{3\}=10^{-2} \times 12.\{3\}=10^{-2} \times 12\frac{3}{9}=10^{-2} \times 12\frac{1}{3}=10^{-2} \times \frac{37}{3}=\frac{37}{300}$$
_________________
Senior Manager
Joined: 06 Jun 2016
Posts: 254
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

### Show Tags

27 Nov 2016, 04:28
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
Non-Human User
Joined: 09 Sep 2013
Posts: 13275
Re: Curly brackets {} around the last digits of a decimal fraction signify  [#permalink]

### Show Tags

22 Feb 2018, 09:10
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Curly brackets {} around the last digits of a decimal fraction signify   [#permalink] 22 Feb 2018, 09:10
Display posts from previous: Sort by