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Intern  Joined: 04 Mar 2009
Posts: 8
If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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11 00:00

Difficulty:   25% (medium)

Question Stats: 72% (01:34) correct 28% (01:38) wrong based on 505 sessions

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If the digits 37 in the decimal 0.00037 repeat indefinitely, what is the value of (10^5-10^3)(0.00037)?

A. 0
B. 0.37 repeating
C. 3.7
D. 10
E. 37

Originally posted by aimingformba on 15 Jul 2010, 22:37.
Last edited by Bunuel on 23 Nov 2012, 09:38, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 59181

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aimingformba wrote:
If the digits 37 in the decimal .00037 repeat indefinitely, what is the value of (105-103)(.00037)?
a. A – 0
b. B – .37 repeating
c. C – 3.7
d. D – 10
e. E – 37

Assuming that answer E (37) is correct, then the question should be:

$$(10^5-10^3)*0.000(37)=?$$

$$(10^5-10^3)*0.000(37)=10^3(10^2-1)*0.00037=99000*0.00(37)$$.

$$0.000(37)=\frac{37}{99000}$$ (see Number Theory chapter of Math Book to know how to convert a recurring decimal to fraction).

So $$99000*0.00(37)=99000*\frac{37}{99000}=37$$.

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Intern  Joined: 16 Jun 2014
Posts: 10
If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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2
Hi guys, for me the following approach made this question easier to handle:

(10^5-10^3)*0.00037 =

(10^5*0.00037) - (10^3*0.00037) =

37.37 - 0.37 =

37
##### General Discussion
Manager  Joined: 16 Apr 2010
Posts: 175

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Hi,

I am not sure about the first part of the equation. Is the question (105-103)*0.00037?

In general, below is the way to solve such questions that have decimals that repeat indefinitely:

1000x = 0.3737
100000x = 37.3737

1000x = 0.3737
100000x - 1000x = 37.3737 - 0.3737
99000x = 37
x = 37/99000

Hope this is of use to you to solve the main question.

regards,
Jack
Intern  Joined: 19 Jul 2009
Posts: 36
Location: baltimore, md
Schools: kellogg, booth, stern, ann arbor

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are the answer choices correct here? i got 74/99000. how is the answer E? any explanations?
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Paaaaayyy Meeeee!!!!!
Intern  Joined: 04 Mar 2009
Posts: 8

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Thanks Bunuel. Sorry for the mess up with the powers...
Intern  Joined: 20 May 2012
Posts: 1

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Hi Bunuel, arent you supposed to do the parenthesis first? so $$(10^5-10^3)$$ becomes $$10^2=100*0.0003737$$..

where am I going wrong here? Intern  Joined: 24 Aug 2005
Posts: 8
Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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Another way to solve is by opening parenthesis and multiplying 0.00037 by 10^5 and then by 10^3. If you notice the fact that 0.00037*10^3 will get rid of repeating 37s, the problem boils down to just multiplying 0.00037 by 10^5
Director  G
Joined: 23 Jan 2013
Posts: 523
Schools: Cambridge'16
Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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Instead of 99000*0.000(37), I just did 100000*0.000(37) and got 37.(37), so the closest is E
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Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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snuffles563 wrote:
Hi Bunuel, arent you supposed to do the parenthesis first? so $$(10^5-10^3)$$ becomes $$10^2=100*0.0003737$$..

where am I going wrong here? This is wrong. $$\frac{10^5}{10^3} = 10^2$$

As far as $$10^5 - 10^3$$ is concerned, $$10^5$$ is way high compared to $$10^3$$

So, $$10^5 - 10^3 \approx10^5$$
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If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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aimingformba wrote:
If the digits 37 in the decimal 0.00037 repeat indefinitely, what is the value of (10^5-10^3)(0.00037)?

A. 0
B. 0.37 repeating
C. 3.7
D. 10
E. 37

Note : Rule to convert mixed recurring decimal to fraction : In the numerator write the entire given number formed by the (recurring and non - recurring parts) and subtract from it the part of the decimal that is not recurring. In the denominator, write as many nines as the number of digits recurring and then place next to it as many zeros as there are digits without recurring in the given decimal.

Converting the mixed recurring decimal ($$0.00037$$) [digits $$37$$ repeat indefinitely] to fraction we get;

$$\frac{37-000}{99000} = \frac{37}{99000}$$

$$(10^5-10^3)(0.00037)$$

$$10^3(10^2-1)(\frac{37}{99000})$$

$$10^3(100-1)(\frac{37}{99000})$$

$$\frac{1000 * 99 * 37}{99000} = 37$$

Intern  B
Joined: 30 Aug 2017
Posts: 5
Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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We can just round it to 0.0004 and check the answer choices!
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9795
Location: Pune, India
Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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aimingformba wrote:
If the digits 37 in the decimal 0.00037 repeat indefinitely, what is the value of (10^5-10^3)(0.00037)?

A. 0
B. 0.37 repeating
C. 3.7
D. 10
E. 37

Note that the answer options are very far apart so some approximation should have no impact.

10^5 is much greater than 10^3 so we can approximate (10^5-10^3) to be just 10^5

10^5 * .000373737 = approx 37.3737...

_________________
Karishma
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GMAT 1: 710 Q48 V40 GMAT 2: 780 Q50 V49 GPA: 4
Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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My approach is as follows:

$$(10^5-10^3)(\frac{37}{99}*10^{-3})$$
$$\implies$$ $$10^3(10^2-1)(\frac{37}{99}*10^{-3})$$
$$\implies$$ $$10^3(10-1)(10+1)(\frac{37}{99}*10^{-3})$$
$$\implies$$ $$10^3*37*10^{-3}$$
$$\implies$$ $$10^0*37=37$$

Kudos are very much appreciated _________________
Good luck to you. Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,   [#permalink] 13 Jan 2019, 11:10
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