NEW HERE? LEARN MORE
closeclose
Last visit was: 05 May 2024, 14:29 It is currently 05 May 2024, 14:29
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If 359/1650 = 0.2175, what is the 100th digit to the right of the deci

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93032
Own Kudos [?]: 621459 [20]
Given Kudos: 81752
Send PM
CAT Tests Forum Quiz Mode
If 359/1650 = 0.2175, what is the 100th digit to the right of the deci [#permalink] New post   22 Oct 2019, 03:22
1
Kudos
19
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

61% (01:44) correct 39% (01:11) wrong based on 197 sessions
Hide Show timer Statistics
If 359/1650 = 0.2175, what is the 100th digit to the right of the decimal point of the fraction?

A. 1
B. 2
C. 5
D. 7
E. 9
ShowHide Answer
Official Answer
C
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6323 [2]
Given Kudos: 704
Location: India
Send PM
If 359/1650 = 0.2175, what is the 100th digit to the right of the deci [#permalink] New post   22 Oct 2019, 19:31
2
Bookmarks
Cyclicity of recurrence decimals of 1/3 is 1
Cyclicity of recurrence decimals of 1/11 is 2

Cyclicity of recurrence decimals of 1/3*11 is LCM(1,2)=2

the 100th digit to the right of the decimal point of the fraction is 5

Or

\(\frac{359*6}{1650*6}\)=\(\frac{2154}{9900}\)= \([21+(\frac{75}{99})] * 10^{-2}\)= .21757575757575......

100th digit to the right of the decimal point= 5


Bunuel wrote:
If 359/1650 = 0.2175, what is the 100th digit to the right of the decimal point of the fraction?

A. 1
B. 2
C. 5
D. 7
E. 9
avatar
B
LidiiaShchichko
Intern
Intern
Joined: 25 Dec 2018
Posts: 14
Own Kudos [?]: 11 [0]
Given Kudos: 432
Send PM
Re: If 359/1650 = 0.2175, what is the 100th digit to the right of the deci [#permalink] New post   22 Oct 2019, 19:47
nick1816 wrote:
Cyclicity of recurrence decimals of 1/3 is 1
Cyclicity of recurrence decimals of 1/11 is 2

Cyclicity of recurrence decimals of 1/3*11 is LCM(1,2)=2

the 100th digit to the right of the decimal point of the fraction is 5

Or

\(\frac{359*6}{1650*6}\)=\(\frac{2154}{9900}\)= \([21+(\frac{75}{99})] * 10^{-2}\)= .21757575757575......

100th digit to the right of the decimal point= 5


Bunuel wrote:
If 359/1650 = 0.2175, what is the 100th digit to the right of the decimal point of the fraction?

A. 1
B. 2
C. 5
D. 7
E. 9



I did't get why do we need cyclicity of 1/33? Could you kindly elaborate?
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6323 [0]
Given Kudos: 704
Location: India
Send PM
Re: If 359/1650 = 0.2175, what is the 100th digit to the right of the deci [#permalink] New post   22 Oct 2019, 19:59
1650= \((2*5^2)*(3*11)\)
Prime numbers except 2 and 5 give repeating decimals. Hence, we have to check the cyclicity of 1/3*11.

LidiiaShchichko wrote:
nick1816 wrote:
Cyclicity of recurrence decimals of 1/3 is 1
Cyclicity of recurrence decimals of 1/11 is 2

Cyclicity of recurrence decimals of 1/3*11 is LCM(1,2)=2

the 100th digit to the right of the decimal point of the fraction is 5

Or

\(\frac{359*6}{1650*6}\)=\(\frac{2154}{9900}\)= \([21+(\frac{75}{99})] * 10^{-2}\)= .21757575757575......

100th digit to the right of the decimal point= 5


Bunuel wrote:
If 359/1650 = 0.2175, what is the 100th digit to the right of the decimal point of the fraction?

A. 1
B. 2
C. 5
D. 7
E. 9



I did't get why do we need cyclicity of 1/33? Could you kindly elaborate?
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11217
Own Kudos [?]: 32285 [3]
Given Kudos: 301
Send PM
Reviews Badge Forum Quiz Mode
Re: If 359/1650 = 0.2175, what is the 100th digit to the right of the deci [#permalink] New post   22 Oct 2019, 21:23
3
Bookmarks
Expert Reply
Bunuel wrote:
If 359/1650 = 0.2175, what is the 100th digit to the right of the decimal point of the fraction?

A. 1
B. 2
C. 5
D. 7
E. 9


\(\frac{359}{1650}=\frac{359*2}{1650*2}=\frac{718}{3300}=\frac{718*3}{3300*3}=\frac{2154}{9900}=\frac{21.54}{99}=\frac{21}{99}+\frac{0.54}{99}=0.212121..+0.0054545=0.21757575...\)
We should be aware that when divided by 99 the numerator (<99) repeats itself. For example - 22/99=0.22.. and 2/99=0.0202..
In 0.217575.. even place in decimals will always be 5

C
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32784
Own Kudos [?]: 827 [0]
Given Kudos: 0
Send PM
Re: If 359/1650 = 0.2175, what is the 100th digit to the right of the deci [#permalink] New post   16 Jan 2024, 23:03
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.
GMAT Club Bot
gmatclubot
Re: If 359/1650 = 0.2175, what is the 100th digit to the right of the deci [#permalink]
16 Jan 2024, 23:03
Moderators:
Bunuel
Math Expert
93033 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions