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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Curly brackets {} around the last digits of a decimal fraction signify

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

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

Show Tags 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 V
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

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

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

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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  