• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for $0 Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

# Any decimal that has only a finite number of nonzero digits

00:00

A

B

C

D

E

## Global Stats

Difficult

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4

Source: Official Guide

OA B

### GMAT/MBA Expert

GMAT Instructor
Joined
22 Aug 2016
Posted:
1385 messages
Followed by:
26 members
470
BTGmoderatorDC wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4

Source: Official Guide

OA B
A ratio, here, r/s is a terminating decimal if s has only two prime factors: 2 and 5.

Note that there is no role of r, so Statement 1 is insufficient.

From Statement 2, we know that s = 4 has a prime factor 2, it's sufficient to collude that r/s is a terminating decimal.

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GMAT Classes San Diego | GRE Prep Course Boston | GRE Prep Chicago | TOEFL Prep Classes NYC | and many more...

### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12121 messages
Followed by:
1237 members
5254
GMAT Score:
770
BTGmoderatorDC wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4

Source: Official Guide

OA B
Target question: Is r/s a terminating decimal?

Statement 1: 90 < r < 100
There are several pairs of values that meet this condition. Here are two:
Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal
Case b: r = 91 and s = 3, in which case r/s = 91/3 = 30.33333.... = a non-terminating decimal
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s = 4
Notice that 1/4 = 0.25, 2/4 = 0.5 and 3/4 = 0.75
So, if the denominator is 4, the resulting decimal will definitely be a terminating decimal.
In other words, if s = 4 then r/s must be a terminating decimal.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Aside: There's a nice rule that says something like,
If the prime factorization of the denominator contains only 2's and/or 5's, then the decimal version of the fraction will be a terminating decimal.
Since the denominator, 4 = (2)(2), the rule tells us that r/s must be a terminating decimal.

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

And check out all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

GMAT Instructor
Joined
04 Dec 2012
Posted:
1903 messages
Followed by:
235 members
1443
Here is further explanation on the logic of terminating decimals:
https://www.beatthegmat.com/ds-decimals-and-ratio-combined-t182983.html#583298

_________________

Ceilidh Erickson
Manhattan Prep GMAT & GRE instructor
EdM in Mind, Brain, and Education

Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
519 messages
Followed by:
25 members
59
BTGmoderatorDC wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4

Source: Official Guide
$r,s\,\, \geqslant 1\,\,\,{\text{ints}}$
$\frac{r}{s}\,\,\,\mathop = \limits^? \,\,\,\,{\text{terminating}}$
$\left( 1 \right)\,\,90 < r < 100\,\,\,\,\left\{ \begin{gathered} \,\left( {r,s} \right) = \left( {95,5} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\left( {\frac{{95}}{5} = \operatorname{int} } \right) \hfill \\ \,\left( {r,s} \right) = \left( {91,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\left( {\frac{{91}}{3} = 30\frac{1}{3} = 30.333 \ldots } \right) \hfill \\ \end{gathered} \right.$

$\left( 2 \right)\,\,s = 4$
$\left( * \right)\,\,\,\,{\text{r/s}}\,\,\,{\text{division}}\,\,{\text{algorithm}}:\,\,\,\left\{ \begin{gathered} \,r = qs + R\,\,\,\mathop = \limits^{s\,\, = \,\,4} \,\,\,4q + R \hfill \\ \,q\,\,\operatorname{int} \,\,\,,\,\,\,\,0\,\,\, \leqslant \,\,\,R\,\,\operatorname{int} \,\,\, \leqslant \,\,3\,\,\,\,\left( { = s - 1} \right) \hfill \\ \end{gathered} \right.$
$\frac{r}{s}\,\,\,\,\mathop = \limits^{\,\left( * \right)} \,\,\,\,\frac{{4q + R}}{4} = q + \frac{R}{4}\,\, = \,\,\operatorname{int} \,\, + \,\,\frac{R}{4}\,\,\,\,\,\,\,$
$\frac{R}{4} = \,\,\,\left\{ {\begin{array}{*{20}{c}} {\,\,\frac{0}{4}} \\ {\,\,\frac{1}{4}} \\ {\,\,\frac{2}{4}} \\ {\,\,\frac{3}{4}} \end{array}} \right.\begin{array}{*{20}{c}} {\,\,{\text{if}}\,\,\,R = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} } \right)} \\ {\,\,{\text{if}}\,\,\,R = 1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.25} \right)} \\ {\,\,{\text{if}}\,\,\,R = 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.5} \right)} \\ {\,\,{\text{if}}\,\,\,R = 3\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.75} \right)} \end{array}$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

### Top Member

Legendary Member
Joined
29 Oct 2017
Posted:
571 messages
Followed by:
4 members
For a fraction to be terminating two conditions must satisfy:
1) numerator is an INTEGER.
2) denominator should be of form 2^x 5^y (x,y => integers which also includes 0).

now in this question
the denominator is 2^2 5^0
hence it satisfies.

Regards!

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
519 messages
Followed by:
25 members
59
swerve wrote:
For a fraction to be terminating two conditions must satisfy:
1) numerator is an INTEGER.
2) denominator should be of form 2^x 5^y (x,y => integers which also includes 0).
Hi swerve!

What about 3/30 ? This number/fraction is terminating (=0.1) but it does not satisfy the conditions you have presented...

Do not forget that for the conditions above, first you must "simplify your fraction"... in other words:

Be sure numerator and denominator are relative prime, then you apply your "laws"!

Regards,
Fabio.

P.S.: curiously, integers x and y MAY be negative... but if so, we are not talking about "denominator", really... therefore I would prefer to add a nonnegative condition on x and y, in your second rule.

_________________
Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

### Top First Responders*

1 Jay@ManhattanReview 84 first replies
2 Brent@GMATPrepNow 73 first replies
3 fskilnik 50 first replies
4 GMATGuruNY 37 first replies
5 Rich.C@EMPOWERgma... 16 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik

GMAT Teacher

199 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

166 posts
3 Scott@TargetTestPrep

Target Test Prep

118 posts
4 Jay@ManhattanReview

Manhattan Review

98 posts
5 Max@Math Revolution

Math Revolution

95 posts
See More Top Beat The GMAT Experts