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# If the digits 37 in the decimal 0.00037 repeat indefinitely,

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Intern
Joined: 04 Mar 2009
Posts: 9
If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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Updated on: 23 Nov 2012, 09:38
1
10
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Difficulty:

25% (medium)

Question Stats:

73% (01:32) correct 27% (01:33) wrong based on 470 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.
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Joined: 02 Sep 2009
Posts: 55228

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16 Jul 2010, 09:00
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: 11
If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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05 Aug 2014, 02:02
11
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: 197

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16 Jul 2010, 05:44
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
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Schools: kellogg, booth, stern, ann arbor

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16 Jul 2010, 08:43
are the answer choices correct here? i got 74/99000. how is the answer E? any explanations?
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Intern
Joined: 04 Mar 2009
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16 Jul 2010, 11:52
Thanks Bunuel. Sorry for the mess up with the powers...
Intern
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23 Nov 2012, 09:24
1
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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23 Nov 2012, 13:20
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
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Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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27 Jul 2014, 22:05
1
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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06 Aug 2014, 02:20
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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18 Jul 2017, 08:20
2
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
Joined: 30 Aug 2017
Posts: 5
Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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14 Dec 2017, 02:40
We can just round it to 0.0004 and check the answer choices!
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Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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14 Dec 2017, 04:02
1
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...

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Karishma
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Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,  [#permalink]

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13 Jan 2019, 11:10
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
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Re: If the digits 37 in the decimal 0.00037 repeat indefinitely,   [#permalink] 13 Jan 2019, 11:10
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