fraction with terminating decimal

Expert replies

vishal.pathak: Master | Next Rank: 500 Posts; Posts: 176; Joined: Thu Sep 22, 2011 5:32 am; Thanked: 5 times

by vishal.pathak » Mon Nov 21, 2011 8:30 am

Which of the following fractions has a decimal equivalent that is a terminating decimal?
A. 10/189 B. 15/196 C. 16/225 D. 25/144 E. 39/128

Is there some way to solve this other than actual evaluation of every option
OA is E

Like this post

Source: Beat The GMAT — Problem Solving | Mon Nov 21, 2011 8:30 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Nov 21, 2011 8:51 am

You get a terminating decimal only when the denominator contains factors of 2 or 5 or 2*5 (in any powers). All other numbers in the denominator produce recurring decimal.eg(3,5,7,9,11 etc)

128 is 2^7. So thats a terminating decimal.

All other options have other numbers in written in their base form (prime numbers raised to power something)

Like this post

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Nov 21, 2011 9:06 am

If a decimal fraction terminates, then it can be written in the form a/100, a/1000, a/10000 and so on

1/(n) is a recurring decimal if n is prime and not equal to 2 or 5

A. 10/189 = 1/3 *(A fraction) = Recurring decimal * A fraction = Recurring decimal
B. 15/196 - 1/7 *(A fraction) = Recurring decimal * A fraction = Recurring decimal
C. 16/225 - 1/3 *(A fraction) = Recurring decimal * A fraction = Recurring decimal
D. 25/144 - 1/3 *(A fraction) = Recurring decimal * A fraction = Recurring decimal
E. 39/128 - Leftover

!

Answer : E

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

Like this post

LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Mon Nov 21, 2011 10:19 am

vishal.pathak wrote:Which of the following fractions has a decimal equivalent that is a terminating decimal?
A. 10/189 B. 15/196 C. 16/225 D. 25/144 E. 39/128

Is there some way to solve this other than actual evaluation of every option
OA is E

my 1st thought was to find a fraction that does not have 3 in the denominator. i just summed all digits of 128 (1+2+8=11) and understood that it is not divisible by 3. as far as I know, any number that has an even number in its denominator is a terminating number.

Like this post

fueledGMAT: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Mon Nov 14, 2011 7:41 am; Location: Colorado Springs, CO; Thanked: 2 times; GMAT Score:690

by fueledGMAT » Mon Nov 21, 2011 11:11 am

shankar.ashwin wrote:You get a terminating decimal only when the denominator contains factors of 2 or 5 or 2*5 (in any powers). All other numbers in the denominator produce recurring decimal.eg(3,5,7,9,11 etc)

128 is 2^7. So thats a terminating decimal.

All other options have other numbers in written in their base form (prime numbers raised to power something)

I will expand on this a bit because of how it is worded...

what shankar means to say is that it will terminate if and ONLY if the prime factorization is a combination of 2s and 5s ONLY. If you have ANY other prime factor in the answer other than a 2 or a 5, the fraction does not terminate...

i.e -
1/8 = 1/(2*2*2) = terminates
1/10 = 1/(2*5) = terminates
1/20 = 1/(2*2*5) = terminates
1/25 = 1/(5*5) = terminates
1/21 = 1/(3*7) = DOES NOT TERMINATE!!
1/60 = 1/(2*3*2*5) = DOES NOT TERMINATE
30/60 = (3*2*5)/(2*3*2*5) = 3's cancel each other out, terminates!

or for a really tough one:
82.5/100 = 825/1000 = (11*3*5*5)/(5*5*5*2*2*2) = terminates! remember, ONLY the denominator matters!

even harder one:
39/130 = (3*13)/(2*5*13) = 13s cancel each other out, only 2s and 5s in denominator... terminates!

"Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away." ~ Antoine de Saint-Exupery

Like this post

chaitanyabhansali: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sun Apr 17, 2011 7:16 amFollowed by: 1 member

by chaitanyabhansali » Tue Nov 22, 2011 11:13 am

to be precise, when you simplify a fraction in its simplest form, then the denominator should contain only 2's and 5's as its factors.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review